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.
[Math] Wave Equation – like 4th Order PDE
partial differential equations
Best Answer
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.