Chapter 6.6, Problem 28P

(a)

To determine

The solution of the Integro differential equation ${\varphi }^{\prime }\left(t\right)+\varphi \left(t\right)={\displaystyle \underset{0}{\overset{t}{\int }}\sin \left(t-\xi \right)}\varphi \left(\xi \right)d\xi ,\varphi \left(0\right)=1$, using Laplace transform.

(b)

To determine

To convert: The integral equation into an initial value problem.

(c)

To determine

To solve: The initial value problem in the sub part (b) and to check whether the obtained solution is same as the one obtained in sub part (a).