I'm trying to solve this equation:(adsbygoogle = window.adsbygoogle || []).push({});

Ux + Uy + U = e^-(x+y) with the initial condition that U(x,0)=0

I played around and and quickly found that U = -e^-(x+y) solves the equation, but does not hold for the initial condition. For the initial condition to hold, I think there needs to be some factor of y in the equation for U, but after trying a few equations, I can't find one that satisfies both the initial condition and the equation.

Can someone throw me a hint?

Thanks!

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# First order PDE help

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