# LaTeX2HTML 95 (Thu Jan 19 1995)
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$key = q/{_inline}$C_2;SPM_lt;C;SPM_lt;C_1${_inline}/;
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$key = q/{displaymath}y'=left((gamma'-deltat)-fracgamma(gamma+delta')deltaright)x+left(fracgamma+delta'deltaright)y,{displaymath}/;
$cached_env_img{$key} ='<A HREF=/cgi-bin/organics/nmpform?mfname=img253.mpl><IMG ALIGN=RIGHT BORDER=0 SRC="../gif/maple/maple253.gif"> </A><A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img253.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img253.gif"></A>'; 
$key = q/{_inline}$beta_C(t)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img11.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img11.gif"></A>'; 
$key = q/{_inline}$u_0(t)=x_0'(t)x_0(t)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img180.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img180.gif"></A>'; 
$key = q/{figure}[h]labelF1vspace1.25invspace6ptpicture(5,5)picture{figure}/;
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$key = q/{displaymath}left[arraycxyarrayright]'=left[arraycc-fracgammadelta;SPM_amp;frac1deltagamma'-deltat-fracgamma(gamma+delta')delta;SPM_amp;fracgamma+delta'deltaarrayright]left[arraycxyarrayright]=left[arraycca;SPM_amp;bc;SPM_amp;darrayright]left[arraycxyarrayright].{displaymath}/;
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$key = q/{_inline}$x(0)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img160.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img160.gif"></A>'; 
$key = q/{figure}[h]labelF9vspace2invspace6ptpicture(5,5)picture{figure}/;
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$key = q/{_inline}$ttoinfty${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img276.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img276.gif"></A>'; 
$key = q/{_inline}$-frac12${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img142.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img142.gif"></A>'; 
$key = q/{_inline}$x''+t^kx=0${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img268.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img268.gif"></A>'; 
$key = q/{_inline}$(partialpartialx)(x^2-t)=2x;SPM_gt;0${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img245.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img245.gif"></A>'; 
$key = q/{_inline}$t_1${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img205.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img205.gif"></A>'; 
$key = q/{_inline}$u(0);SPM_lt;u_0(0)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img197.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img197.gif"></A>'; 
$key = q/{_inline}$y=x'+x2t${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img266.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img266.gif"></A>'; 
$key = q/{_inline}$u(0);SPM_gt;u_0(0)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img207.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img207.gif"></A>'; 
$key = q/{_inline}$ntoinfty${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img133.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img133.gif"></A>'; 
$key = q/{_inline}$-infty${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img39.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img39.gif"></A>'; 
$key = q/{_inline}$u_0(0)=0.729011132dots${_inline}/;
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$key = q/{_inline}$x'=x^2-t${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img239.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img239.gif"></A>'; 
$key = q/{_inline}$n=-12${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img264.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img264.gif"></A>'; 
$key = q/{_inline}$tge0${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img244.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img244.gif"></A>'; 
$key = q/{_inline}$t^12${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img240.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img240.gif"></A>'; 
$key = q/{_inline}$y(0)approx-0.729${_inline}/;
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$key = q/{_inline}$pi2${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img117.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img117.gif"></A>'; 
$key = q/{displaymath}gamma(t)=-frac14t^-32quadmboxandquaddelta(t)=-frac1sqrtt,{displaymath}/;
$cached_env_img{$key} ='<A HREF=/cgi-bin/organics/nmpform?mfname=img265.mpl><IMG ALIGN=RIGHT BORDER=0 SRC="../gif/maple/maple265.gif"> </A><A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img265.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img265.gif"></A>'; 
$key = q/{_inline}$x''=-tx${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img80.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img80.gif"></A>'; 
$key = q/{_inline}$x(0)=-1${_inline}/;
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$key = q/{_inline}$y=gamma(t)x+delta(t)x'${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img75.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img75.gif"></A>'; 
$key = q/{figure}[h]labelF3vspace2.5invspace6ptpicture(5,5)picture{figure}/;
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$key = q/{figure}[h]labelF2vspace2invspace6ptpicture(5,5)picture{figure}/;
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$key = q/{_inline}$x'=f(t,x)${_inline}/;
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$key = q/{_inline}$r'r${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img138.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img138.gif"></A>'; 
$key = q/{_inline}$UsubsetRe^2${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img271.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img271.gif"></A>'; 
$key = q/{displaymath}-gamma=gamma+delta',quadmboxorquadgamma=-fracdelta'2=fracn2t^n-1.{displaymath}/;
$cached_env_img{$key} ='<A HREF=/cgi-bin/organics/nmpform?mfname=img259.mpl><IMG ALIGN=RIGHT BORDER=0 SRC="../gif/maple/maple259.gif"> </A><A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img259.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img259.gif"></A>'; 
$key = q/{_inline}$delta(t)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img256.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img256.gif"></A>'; 
$key = q/{_inline}$int_1^inftyw(t)dt;SPM_gt;-infty${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img275.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img275.gif"></A>'; 
$key = q/{_inline}$-sqrt|t|${_inline}/;
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$key = q/{_inline}$tto-infty${_inline}/;
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$key = q/{_inline}$x=-sqrtt${_inline}/;
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$key = q/{_inline}$-sqrt|t|-1${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img198.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img198.gif"></A>'; 
$key = q/{_inline}$-t^n${_inline}/;
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$key = q/{_inline}$x(0.1)=0${_inline}/;
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$key = q/{_inline}$delta${_inline}/;
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$key = q/{_inline}$gamma(t)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img255.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img255.gif"></A>'; 
$key = q/{_inline}$t-;SPM_gt;infty${_inline}/;
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$key = q/{_inline}$x(t)${_inline}/;
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$key = q/{_inline}$x(t)=0${_inline}/;
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$key = q/{_inline}$C_2${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img281.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img281.gif"></A>'; 
$key = q/{_inline}$C_1${_inline}/;
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$key = q/{_inline}$beta'_C(t)ge${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img99.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img99.gif"></A>'; 
$key = q/{_inline}$w(t)${_inline}/;
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$key = q/{_inline}$(x(t),y(t))${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img28.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img28.gif"></A>'; 
$key = q/{figure}[h]labelF4vspace1.25invspace6ptpicture(5,5)picture{figure}/;
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$key = q/{_inline}$Gamma${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img48.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img48.gif"></A>'; 
$key = q/{_inline}$|t_n-t_n-1|${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img135.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img135.gif"></A>'; 
$key = q/{_inline}$C_2=-infty${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img284.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img284.gif"></A>'; 
$key = q/{_inline}$Kt^-14${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img146.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img146.gif"></A>'; 
$key = q/{_inline}$U_C${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img103.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img103.gif"></A>'; 
$key = q/{_inline}$C_1=C_2${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img286.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img286.gif"></A>'; 
$key = q/{displaymath}x_0(t)simCe^-frac23|t|^32.{displaymath}/;
$cached_env_img{$key} ='<A HREF=/cgi-bin/organics/nmpform?mfname=img186.mpl><IMG ALIGN=RIGHT BORDER=0 SRC="../gif/maple/maple186.gif"> </A><A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img186.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img186.gif"></A>'; 
$key = q/{figure}labelF7vspace2.75invspace6ptpicture(5,5)picture{figure}/;
$cached_env_img{$key} ='<A HREF=/cgi-bin/organics/nmpform?mfname=img126.mpl><IMG ALIGN=RIGHT BORDER=0 SRC="../gif/maple/maple126.gif"> </A><A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img126.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img126.gif"></A>'; 
$key = q/{figure}labelF5vspace1.75invspace6ptpicture(5,5)picture{figure}/;
$cached_env_img{$key} ='<A HREF=/cgi-bin/organics/nmpform?mfname=img90.mpl><IMG ALIGN=RIGHT BORDER=0 SRC="../gif/maple/maple90.gif"> </A><A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img90.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img90.gif"></A>'; 
$key = q/{figure}[h]labelF13vspace2.5invspace6ptpicture(5,5)picture{figure}/;
$cached_env_img{$key} ='<A HREF=/cgi-bin/organics/nmpform?mfname=img230.mpl><IMG ALIGN=RIGHT BORDER=0 SRC="../gif/maple/maple230.gif"> </A><A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img230.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img230.gif"></A>'; 
$key = q/{_inline}$x;SPM_lt;-1-e^-4${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img225.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img225.gif"></A>'; 
$key = q/{_inline}$u(t)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img206.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img206.gif"></A>'; 
$key = q/{_inline}$frac12${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img143.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img143.gif"></A>'; 
$key = q/{_inline}$x=-sqrtt-1${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img236.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img236.gif"></A>'; 
$key = q/{figure}[h]labelF6vspace2.875invspace6ptpicture(5,5)picture{figure}/;
$cached_env_img{$key} ='<A HREF=/cgi-bin/organics/nmpform?mfname=img112.mpl><IMG ALIGN=RIGHT BORDER=0 SRC="../gif/maple/maple112.gif"> </A><A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img112.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img112.gif"></A>'; 
$key = q/{_inline}$t_n${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img127.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img127.gif"></A>'; 
$key = q/{_inline}$x_0(t)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img184.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img184.gif"></A>'; 
$key = q/{_inline}$u_0(0)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img191.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img191.gif"></A>'; 
$key = q/{_inline}$x=sqrtt${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img242.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img242.gif"></A>'; 
$key = q/{figure}[h]labelF12vspace2.5invspace6ptpicture(5,5)picture{figure}/;
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$key = q/{_inline}$x''${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img250.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img250.gif"></A>'; 
$key = q/{_inline}$beta(t)=sqrt|t|+1${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img178.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img178.gif"></A>'; 
$key = q/{_inline}$(partialfpartialx)(t,x)gew(t)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img274.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img274.gif"></A>'; 
$key = q/{displaymath}x''+frac1tx'+left(1-fracn^2t^2right)x=0.{displaymath}/;
$cached_env_img{$key} ='<A HREF=/cgi-bin/organics/nmpform?mfname=img267.mpl><IMG ALIGN=RIGHT BORDER=0 SRC="../gif/maple/maple267.gif"> </A><A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img267.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img267.gif"></A>'; 
$key = q/{_inline}$u_0(t)=x'_0(t)x_0(t)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img187.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img187.gif"></A>'; 
$key = q/{figure}[h]labelF8vspace1.25invspace6ptpicture(5,5)picture{figure}/;
$cached_env_img{$key} ='<A HREF=/cgi-bin/organics/nmpform?mfname=img158.mpl><IMG ALIGN=RIGHT BORDER=0 SRC="../gif/maple/maple158.gif"> </A><A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img158.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img158.gif"></A>'; 
$key = q/{_inline}$t;SPM_gt;t_C${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img211.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img211.gif"></A>'; 
$key = q/{_inline}$-sqrtt;SPM_lt;u(t);SPM_lt;-sqrt(t-1)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img234.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img234.gif"></A>'; 
$key = q/{_inline}$x'=x^2-1+e^-t^2${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img20.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img20.gif"></A>'; 
$key = q/{displaymath}t^n+1+left(fracn^24-fracn2right)t^n-2;{displaymath}/;
$cached_env_img{$key} ='<A HREF=/cgi-bin/organics/nmpform?mfname=img262.mpl><IMG ALIGN=RIGHT BORDER=0 SRC="../gif/maple/maple262.gif"> </A><A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img262.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img262.gif"></A>'; 
$key = q/{_inline}$beta_C${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img293.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img293.gif"></A>'; 
$key = q/{_inline}$gamma${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img76.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img76.gif"></A>'; 
$key = q/{_inline}$u'=-u^2-t${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img173.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img173.gif"></A>'; 
$key = q/{displaymath}t_nsimleft{frac32left[frac(2n+1)pi2-Cright]right}^23.{displaymath}/;
$cached_env_img{$key} ='<A HREF=/cgi-bin/organics/nmpform?mfname=img134.mpl><IMG ALIGN=RIGHT BORDER=0 SRC="../gif/maple/maple134.gif"> </A><A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img134.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img134.gif"></A>'; 
$key = q/{_inline}$r(t)^2=x(t)^2+y(t)^2${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img55.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img55.gif"></A>'; 
$key = q/{_inline}$r(t)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img150.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img150.gif"></A>'; 
$key = q/{_inline}$u_0(t)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img176.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img176.gif"></A>'; 
$key = q/{figure}[h]labelF11vspace2.5invspace6ptpicture(5,5)picture{figure}/;
$cached_env_img{$key} ='<A HREF=/cgi-bin/organics/nmpform?mfname=img219.mpl><IMG ALIGN=RIGHT BORDER=0 SRC="../gif/maple/maple219.gif"> </A><A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img219.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img219.gif"></A>'; 
$key = q/{_inline}$x'(0)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img161.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img161.gif"></A>'; 
$key = q/{_inline}$-sqrt1-e^-t^2${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img221.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img221.gif"></A>'; 
$key = q/{_inline}$x(0)=-1,x'(0)=0.729dots${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img193.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img193.gif"></A>'; 
$key = q/{_inline}$x=sqrtt+1${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img243.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img243.gif"></A>'; 
$key = q/{_inline}$x'${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img248.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img248.gif"></A>'; 
$key = q/{_inline}$t^-14${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img148.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img148.gif"></A>'; 
$key = q/{displaymath}gamma'-deltat-fracgamma(gamma+delta')deltaquadmboxandquadfrac1delta=-t^-n{displaymath}/;
$cached_env_img{$key} ='<A HREF=/cgi-bin/organics/nmpform?mfname=img260.mpl><IMG ALIGN=RIGHT BORDER=0 SRC="../gif/maple/maple260.gif"> </A><A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img260.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img260.gif"></A>'; 
$key = q/{figure}[h]labelF10vspace2.75invspace6ptpicture(5,5)picture{figure}/;
$cached_env_img{$key} ='<A HREF=/cgi-bin/organics/nmpform?mfname=img306.mpl><IMG ALIGN=RIGHT BORDER=0 SRC="../gif/maple/maple306.gif"> </A><A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img306.tex"  ><IMG BORDER=0 ALIGN=BOTTOM ALT=""" SRC="../gif/img306.gif"></A>'; 
$key = q/{_inline}$y=x'${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img73.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img73.gif"></A>'; 
$key = q/{_inline}$x''+tx=0${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img61.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img61.gif"></A>'; 
$key = q/{_inline}$C_1=infty${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img283.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img283.gif"></A>'; 
$key = q/{_inline}$x'=x^2-1+e^-t${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img226.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img226.gif"></A>'; 
$key = q/{_inline}$beta_C_2(t)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img22.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img22.gif"></A>'; 
$key = q/{_inline}$x(0)=0${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img163.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img163.gif"></A>'; 
$key = q/{_inline}$partialfpartialx;SPM_gt;0${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img238.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img238.gif"></A>'; 
$key = q/{_inline}$C_1neC_2${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img289.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img289.gif"></A>'; 
$key = q/{_inline}$y(0)=x'(0)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img159.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img159.gif"></A>'; 
$key = q/{_inline}$C_1geC_2${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img285.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img285.gif"></A>'; 
$key = q/{_inline}$t;SPM_gt;=54${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img237.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img237.gif"></A>'; 
$key = q/{_inline}$+infty${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img40.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img40.gif"></A>'; 
$key = q/{_inline}$x'(0.1)=1${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img8.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img8.gif"></A>'; 
$key = q/{_inline}$x''+x=0${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img25.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img25.gif"></A>'; 
$key = q/{_inline}$(t,x)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img224.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img224.gif"></A>'; 
$key = q/{_inline}$t=-9,u=sqrt10${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img189.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img189.gif"></A>'; 
$key = q/{_inline}$w(t)=-frac58t^-52${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img278.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img278.gif"></A>'; 
$key = q/{_inline}$-t^-n${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img263.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img263.gif"></A>'; 
$key = q/{_inline}$u(2);SPM_lt;-1${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img233.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img233.gif"></A>'; 
$key = q/{_inline}$t_C;SPM_lt;0${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img209.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img209.gif"></A>'; 
$key = q/{_inline}$u(t)=y(t)x(t)${_inline}/;
$cached_env_img{$key} ='<A HREF="/cgi-bin/organics/evaleqn.pl?tfname=img29.tex"  ><IMG BORDER=0 ALIGN=MIDDLE ALT=""" SRC="../gif/img29.gif"></A>'; 

1;

