Chapter 2.3, Problem 34E

To determine

(a)

To Prove:

The function $\mu \left(x\right)$ is positive, continuous function in $\left(a,b\right)$ satisfying,

$\frac{d\mu }{dx}=P\left(x\right)\mu \left(x\right)$.

To determine

(b)

To prove:

That $y\left(x\right)$ is a solution to the ordinary differential equation.

To determine

(c)

To prove:

The given anti-derivative satisfies the initial conditions.

To determine

(d)

To find:

The condition to determine the constant uniquely.