Question: Suppose a function $f(x, y)$ can be expressed as the product of two functions, $g(x)$ and $h(y)$. Use separation of variables to solve the following differential equation:

Answer: We are given the differential equation $y' = \frac{x^2}{y-1}$ and we want to solve it using separation of variables.

First, we express $f(x, y)$ as the product of two functions:

We can rewrite the differential equation as follows:

Now, we proceed with separating the variables:

We can now integrate both sides with respect to their respective variables:

Here, $C$ is the constant of integration.

So, the general solution is given by:

This is our solution using separation of variables.