# Simple 1st order PDE [duplicate]

Solve $u_x+u_y+u=e^{x+2y}$ with $u(x,0)=0$

I try to let $x'=x+y, y'=x-y$ and reduced to $2u_{x'}+u=e^{0.5(3x'-y)}$

How to proceed to the next step? Any other methods to solve?

Thank you!

• $$2u_{x'} + u = \exp \bigg( \frac{1}{2} (3x'-y) \bigg)$$ is an ODE in $x'$. You could use an integrating factor. Alternatively, you could solve the problem using the method of characteristics. – mattos Dec 1 '16 at 14:07