Example 5

Find the solution of the initial value problem

y' + y ln (2 + cos t) = t, y(1) = 4.

We are not able to evaluate the integral of ln (2 + cos t), so we shall use the definite integral form of the solution. With the initial point a = 1, the solution is

We conclude this section with a proof of Theorem 1. The proof uses the Principle of Superposition.