Im working through some problems in Strauss book on PDE. I can't find a good method to solve the following:
$3u_x + u_{xy} = 0$. Where $u=u(x,y)$ and $u_x$ denotes the partial w.r.t $x$.
Now, the text provides no discussion on equations of this form. My instinct says to integrate over $x$ and solve the result as an ODE of a function of $y$. This is the second problem in the book though and it seems there should be a more direct approach. Any ideas?