
1302 LINEAR PARTIAL DIFFERENTIAL EQUATIONS WITH MAPLE
with(PDEtools): declare(u(x,y),W(x,y),phi(x),psi(y));
interface(showassumed=0): assume(n,'integer',n>0): tr1:=phi(x)*psi(y);
PDE1:=u->a*diff(u(x,y),x) +b*diff(u(x,y),y); IC1:= u(0,y)=alpha*exp(-beta*y);
Eq2:=expand(PDE1(W)); Eq3:=expand(subs(W(x,y)=tr1,Eq2));
Eq4:=expand(Eq3/phi(x)/psi(y)); Eq5:=isolate(Eq4,psi(y));
Eq61:=rhs(Eq5)=_C1; Eq62:=lhs(Eq5)=_C1;
Then we seek exact solutions of these eq uations as follows:
Sol1:=dsolve(Eq61,phi(x)); Sol2:=dsolve(Eq62,psi(y));
GenSol:=u(x,y)=simplify(subs(Sol1,Sol2,tr1)); trC3:=_C2ˆ2=_C3;
GenSol1:=subs(trC3,GenSol); Eq8:=subs(x=0,rhs(GenSol1))=rhs(IC1);
trC13:=_C1=-beta, ...