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I have a very simple example of a second order PDE:

eqn = D[u[x, y], x, y] + u[x, y] == 0;
sol = DSolve[eqn, u, {x, y}]

and Mathematica cannot solve it! What is wrong!?

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In the tutorial on second-order PDE's it says "DSolve can find the general solution for a restricted type of homogeneous linear second-order PDEs..." Unfortunately this equation is not of that type (it has a non-vanishing non-principal part). So I don't think there's anything wrong as such, it's just that Mathematica can't solve this PDE. –  Simon Woods Mar 26 '13 at 20:48

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