1
$\begingroup$

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?

  • 0
    @RobertIsrael ah, but fortunately I did not say they were constant :)2012-09-06

1 Answers 1

5

Actually I'd go the other way. Solve $3 U_x + \dfrac{\partial}{\partial y} U_x = 0$ to get $U_x = C(x) e^{-3y}$. Then integrate with respect to $x$ (remembering that the "constant" of integration can depend on $y$).