# Wave Equation - like 4th Order PDE

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.

• Well, you can use the good old method of se – RougeSegwayUser Sep 11 '12 at 4:10
• 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

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