Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
$3D_x+D_{xy} = D_x(3+D_y)$ hence $u(x,y)=c_1+c_2e^{-3y}$... did I miss anything? – James S. Cook Sep 6 '12 at 18:13
@JamesS.Cook: yes, you did. The "constants" are not constant. – Robert Israel Sep 6 '12 at 18:18
@RobertIsrael ah, but fortunately I did not say they were constant :) – James S. Cook Sep 6 '12 at 18:22
up vote 5 down vote accepted

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 $y$).

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.