Question

Can this Partial Differential Equation be solved by Separation of Variables?

Utt(2nd PD wrt to t) + (t^2 + x^2)Uxx = 0
Justify your answer please.

Answer 1

Try putting U = F(t)G(x) and see if you can use separation of variables. I don't think you can do due to (t^2 + x^2).

Try method called Monge's method.

Answer 2

\[U_{tt} + (t^2 + x^2)U_{xx} = 0\]
\[\frac{\partial^2 U}{\partial t^2} + (t^2 + x^2)\frac{\partial^2U}{\partial x^2} = 0\]