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Student Support Forum: 'Solving PDEs with ICs' topicStudent Support Forum > General > Archives > "Solving PDEs with ICs"

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Author Comment/Response
Jim Kochanski
02/10/12 4:57pm

I have successfully solved a number of ODEs and PDEs with and without ICs using Mathematica 8.

Following is the second PDE I was unable to solve using same approaches that proved successful before. (First is the PDE successfully solved without ICs; then the PDE unsuccessfully solved with ICs. NOTE: After cut-and-paste, blank spaces were removed for brevity.)

Any suggestions or insight would be greatly appreciated.

Success without ICs:
Input
DSolve[D[D[U[x,t],t],t]-9 D[D[U[x,t],x],x]==0,U[x,t],{x,t}]
Output
{{U[x,t]->C[1][t-x/3]+C[2][t+x/3]}}

No Success with ICs:
Input
DSolve[{D[D[U[x,t],t],t]-9 D[D[U[x,t],x],x]==0,U[x,0]==ArcTan[x],D[U[x,t],t]==2 x Log[1+x^2]},U[x,t],{x,t}]
Output
DSolve[{(U^(0,2))[x,t]-9 (U^(2,0))[x,t]==0,U[x,0]==ArcTan[x],(U^(0,1))[x,t]==2 x Log[1+x^2]},U[x,t],{x,t}]


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