# Homework Help: 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.

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