Tell me more ×
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.
up vote 1 down vote favorite

How does one solve a fourth-order PDE of the form $\frac{\partial^4y}{\partial x^4}=c^2\frac{\partial^2y}{\partial t^2}$? It looks like a one dimensional wave equation, but I'm unfortunately very bad at PDEs.

share|improve this question
Well, you can use the good old method of se – Chris Dugale Sep 11 '12 at 4:10
1  
As Chris was saying, just suppose $y(x,t)=X(x)T(t)$ and subsitute that into the problem to obtain $X''''T=c^2XT''$. Divide by $XT$ etc... – James S. Cook Sep 11 '12 at 4:17

1 Answer

up vote 2 down vote accepted

You do almost the same thing as people explained in your other question. Unfortunately, you can only factor the operator into

$$ \left(\frac{\partial^2}{\partial x^2} - c\frac{\partial}{\partial t}\right) \left(\frac{\partial^2}{\partial x^2} + c\frac{\partial}{\partial t}\right)y = 0. $$

Then you have to solve a heat-equation like equation.

If your domain is finite, you should try separation of variables.

share|improve this answer

Your Answer

 
discard

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.