Solve homogeneous first order PDE's

1. Sep 10, 2006

Dragonfall

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

I have no idea how to do this. We were only taught how to solve homogeneous first order PDE's.

2. Sep 10, 2006

Dr Transport

try separating variables...

3. Sep 10, 2006

Dragonfall

What do you mean?

4. Sep 13, 2006

Dragonfall

I am getting nowhere with this. I tried using the method of characteristics, but it doesn't work out.

5. Sep 13, 2006

J77

Write $$u(x,y)=X(x)Y(y)$$, plug this into you equation and...

Note also: $$e^{x+2y}=e^xe^{2y}$$

6. Sep 13, 2006

Dragonfall

How do you know that u actually can be written as X(x)Y(y)?

7. Sep 13, 2006

d_leet

I think that it's more or less an assumption we make when dealing with homogenous PDEs, but I'm probably completely wrong on this.