MVR5
I$ode=6"%&falseGE\[l6%7indvarchange/varchangeGR6(%%deqnG%%TeqnG%"tG%"TG%%tsolG%
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@$-%'isdiffG6#F<C&>8&-%'depvarGFA>F<-%2indvarchange/diffG6'-%%subsG6$/9&9'FD9%F
OFP-%*difforderGFA>F<-%;indvarchange/subs/nondiffsG6$/FO9(F<-%'RETURNGFA>8)<#-%
#opGFA>8*-%'selectG6%%$hasGFgn%%diffG>8+-%&minusG6$FgnF\o?&8$Fco%%trueG>Fco-%&u
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FD-FFFar>Fho-FI6'FKFQFOFP-FSFar>Fho-FV6$FXFho>F<-%'subsopG6$/FfqFhoF</FhoFO>F<-
F^s6$/FfqFYF<-F`o6$FhoFO@%32F\r-F_q6#Fbp5-%'memberG6$FhoFbp-F_t6$F_pFbp>F<-F^s6
$/Ffq-FL6$FNFhoF<C$>Fho-9!6(FhoFQFOFPFYFjp>F<F]sFZF$F$F$%-indvarchangeGR6&F*'F+
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%::~deqn~does~not~contain~'GFO%:'~as~independent~variableG@&4-F`o6$FQFO-F`v6#((
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o@$/FcoF]y>FcoF]q@$50F<-%,maxPDEorderG6#Fco0FD-%'degreeGFc_lC'>F<Fa_l>FDFe_l>&F
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F\]lR6#'Fc[l<$/FizFizFiz6,%"mG%"LG%"cG%"dG%$ansG%"vGF1%$tmpGFb[lF][lF$F$C->F<-%
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R6$FhuFc[l6&F6F1F9%(newexprGF$F$C%>FbpFQ@$4-F@6#FQC%>Fho7#-FjnFbem>FbpFQ?&F<Fho
Fio@$2F\r-F_q6#-%'indetsGFA@$4F?C$>FD-Fhq6$FbpF<@$2F\rF^]mC$@%/-F_qFAF]q>F<-FL6
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ho-FjxFbw@$4-F`o6$F=FP-F`v6#(%V:~expr~does~not~contain~the~new~independent~vari
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GFO>F<F=@$3Fiw2F]qF_x>F<-F\u6'F<FQFOFP,&F_xF]qF`pF]q@%Fas,&-Fao6$F<FOF]q*&-Fao6
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F$C&>F\qFabl>FbpF=?&FhoFbpFio@$F_[nC$>F<-F^o6%F`oFhoFao@$-F`o6$F<FaoC$>FDFcfm@&
FffmC$>F<-F`cl6%F<FaoF\q>FbpFagm-Fhp6$F<Fijl?&FgnF<FioC$>FD-Fhq6$FbpFgn@$FffmC$
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F^[n-F`v6#%^o:~one~or~more~of~deqns~is~not~a~differential~equation~or~expressio
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4Facn>F<7#F<>FDFb^l?&FhoF<FioC$>Fho-FL6$FQFho>FD7$F`dmFho@%/F^]mF]qF`dmFDF$F$F$
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sformed~equations:G""%F`bl>83-F_q6#F`bl-Fddl6%F\u%;forming~global~equation...GF
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u%1global~equation:GFdgnFbp-Fddl6%F\u%?decomposing~global~equation...GF\r>Fgn-F
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j^lFdx>Fb[o-F\p6$Fb[o<#&Fj^l6#-F_q6#Fj^lC$>Fco-F\p6$Fco-F\^l6$F[blFdx>Fb[o-F\p6
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1~coefficients...GF\r?(F\qF]qF]qFfgnFio>&F<Fdq-%)GetCoeffG6&Fgn&FcoFdqFcfnFb[o-
Fddl6&F\u((%7coefficients~of~order~GFcfn%.~derivatives:GFefn-F\^l6$F<Fdx-Fddl6%
F\u%Osolving~coefficients~to~isolate~derivatives...GF\r?(F\qF]qF]qFfgnFioC1-Fdd
l6&F\u((%6isolating~derivative~GF\qFchnF]q-Fao6$F``o-F]fl6$Fb[oFcfn?(Ff`lF]qF]q
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F$&&F=6#F\al6#-F_el6&F=FQFOFPF$F$F$FFRFbcmFe[oF$F$C$>Fho-F_\mFi\l-Fen6#&FhoF^il
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n6#-FSFi\l@$/-F_qFi\lF]q-Fen6#F\r>F<F\r?&FhoF=Fio@%F`r>F<-%$maxG6$F<Fhr>F<-Fijo
6$F<-F\uFarFZF$F$F$F^^lR6$F1Fb[l6%%"aG%"bGFfflF$F$C'>Fho-F^o6%F`o*&F=F]qFDF]qFa
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F]qF]qF$-FhpF_^nC$>Fho,&FhoF]qF]qF]q>F<Fddm-FenFarF$F$F$F$