Originally Posted by

**dlbsd** Hi, I just started studying PDE's so sorry for the newbie questions

I have two questions

1. Solve

$\displaystyle au_x + bu_y + cu = 0$

2. Solve

$\displaystyle u_x + u_y = 1$

Here is what I have so far for #1:

Using change of variables

$\displaystyle x' = ax + by$

$\displaystyle y' = bx - ay$

$\displaystyle u_x = au_{x'} + bu_{y'}$

$\displaystyle u_y = bu_{x'} - au_{y'}$

$\displaystyle a(au_{x'} + bu_{y'}) + b(bu_{x'} - au_{y'}) + cu = 0$

$\displaystyle (a^2 + b^2)u_{x'} + cu = 0$

This is where I get stuck. How do i solve for u in this case?

For #2, I'm not sure how to start but I want to say its unsolvable because its inhomogeneous? (probably way wrong in saying that haha)