Help please, I need to solve this differential equation $\displaystyle x\frac{\partial^2 U}{\partial x^2}+y\frac{\partial^2 U}{\partial y^2}=aU$ in Matlab (where "a" is a constant parameter, it can be taken by any), I wanted to use the Partial Differential Equation Toolbox, but I ran into a problem, the elliptic equation in this Toolbox is represented in a vector form, namely -div(c*grad(u))+a*u=f.

Please help me convert my equation to this form and tell me how it can be done or at least name the sources of information from which I can learn this knowledge.

I really need to solve this equation in Matlab,so please tell me how it can be done.