Form Partial Differential Equation

Question

z=A exp(pt) sin (px)

Form pde for the above equation where A and p are arbitrary constants

x ,t independent variable Z = f(x,t)

Answer 1

$$Z(x,t)=Ae^{pt}\sin(px)$$ $$\frac{\partial Z}{\partial t}=pZ$$ $$\frac{\partial^2 Z}{\partial x^2}=-p^2Z$$ $$\left(\frac{\partial Z}{\partial t}\right)^2=-Z\frac{\partial^2 Z}{\partial x^2}$$