Complete solution or General solution of PDE

Question

I am a research student of Mathematical physics. I am looking a generalization to find a complete or general solution of Partial Differential Equations in the form of:

$$\frac{\partial^2M}{\partial t\partial x} = F\left(M, \frac{\partial M}{\partial t}, \frac{\partial M}{\partial x}, \frac{\partial^2M}{\partial x^2}\right).$$

I need the generalization with suitable example.

for the better understanding I am looking general solution for the following question.

1. Find general solution of $∂^2$M/∂t∂x = M($∂^2$M/$∂t^2$)

Thank you all.