Separation of variables, Schrodinger's Equation.
For the first part of a physics homework question, I am given an equation and am told to separate the variables in a certain way. I am pretty sure this is part of ordinary differential equations, which I have never learned. (Not a pre- or co-requisite of my course.) Here is what I am asked - any help would be appreciated! Thank you!

The Schrodinger equation for two dimensions is $$(\frac{\delta ^2}{\delta x^2} \frac{\delta ^2}{\delta y^2}) \psi (x,y) = - \frac{2m(E-U)}{\hbar ^2} \psi (x,y)$$
U is constant.

I am supposed to "separate variables by trying a solution of the form ψ(x,y)=f(x)g(y)
then dividing by f(x)g(y)." It also says to call the separation constants $$C_x$$and$$C_y$$

Question

Separation of variables, Schrodinger's Equation.
For the first part of a physics homework question, I am given an equation and am told to separate the variables in a certain way. I am pretty sure this is part of ordinary differential equations, which I have never learned. (Not a pre- or co-requisite of my course.) Here is what I am asked - any help would be appreciated! Thank you!

The Schrodinger equation for two dimensions is $$(\frac{\delta ^2}{\delta x^2} \frac{\delta ^2}{\delta y^2}) \psi (x,y) = - \frac{2m(E-U)}{\hbar ^2} \psi (x,y)$$
U is constant.

I am supposed to "separate variables by trying a solution of the form ψ(x,y)=f(x)g(y) 
then dividing by f(x)g(y)." It also says to call the separation constants $$C_x$$and$$C_y$$