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First-order PDE with side condition

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  • Subject: [mg120952] First-order PDE with side condition
  • From: James <icorone at>
  • Date: Thu, 18 Aug 2011 03:24:21 -0400 (EDT)
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Hi guys,

I'd like to check my analytic solution of the following PDE using NDSolve.  The initial condition is a side-condition on the line y=ex/3 and I don't know how to set up NDSolve for that:

e^(-x)u_x+1/(y^2) u_y-e^(x) y u=0;    u(x,ex/3)=e

Here's a start setting up NDSolve which I know is not correct. Maybe I need to use the method of lines and specify a temporal variable.  Not sure and didn't see any examples for that in the PDE info for NDSolve.  I'm hoping someone could help me fix it.

NDSolve[{Exp[-x]*D[u[x, y], x] + D[u[x, y], y]/
      y^2 - Exp[x]*y*u[x, y] == 0, 
   u[x, (E*x)/3] == E}, u, {x, 0, 1}, {y, 0, 1}]

Thanks guys.

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