The given differential equation is:
To solve this equation by separation of variables, we can first move the term to the left-hand side and the term to the right-hand side, giving:
Now, we can integrate both sides. On the left-hand side, the integral becomes as.
Where is the constant of integration.
On the right-hand side, we can integrate, so the integral becomes:
(4)where is another constant of integration.
Putting the two integrals together, we have:
where is the constant of integration.