Problem

Solve the following differential equation by separation of variables.

Use the initial condition

to solve for the unique solution.

Solution

We multiply and divide as needed to get the terms containing y on the left hand side of the equation and the terms containing x on the right hand side.

Then integrate both sides and solve for y. At each step that involves a constant, we absorb earlier versions of the constant into a new version.

Now use the initial condition and solve for the constant.

Therefore

and the unique solution to the differential equation is