Hi the question I have to solve is:
$u_x + u_y + u = e^{x+2y} \ $ where $ u(x,0) = 0$
First, I tried to solve the question of the form:
$$ u_x + u_y + u = 0$$
We know that $\dot x = 1 \ $ and $\dot y = 1 \ $. From that we can introduce s where $$x(s) = s +x_0$$ and $$y(s) = s$$. Then if $z = u(x(s), y(s))$ we have that $\dot z + z = 0$.
By setting $s = y$ we have then that $x_0 = y-x$.
Then we can get that $u(x,y) = e^{-y} \ g(y-x)$.
Now, to get $\dot z + z = e^{x+2y}$ I am completely stuck
