#### Find the complete solution of the differential equation .

**SOLUTION:**

By cross-multiplication,

Factor out common monomial factors

Simplify

Combine all terms with x, and combine all terms with y

Since the variables are already separated, we can already apply integration. That is,

For

Let u=.

For .

Let u=

Combining the solutions, we come up with

We can simplify the solution further by applying the law of logarithms. That is

That is already an acceptable answer, but we can still simplify it further by eliminating the natural logarithm.

However, is also a constant so we can name it to another constant, say . So,

That is also an acceptable answer but we can still simplify the equation by eliminating the square root sign. That is

However, is another constant and we can rename it to . That is,

Simplifying,