Chapter D1.4, Problem 43E

a.

To determine

To show: The differential equation $y^{\prime }\left(t\right)=\frac{y{\left(t\right)}^p}{1-p}{v}^{\prime }\left(t\right)$ by letting $v=y^{1-p}$.

b.

To determine

To solve: The differential equation $y^{\prime }\left(t\right)+ay=b{y}^p$ by substitute the value of $y^{\prime }\left(t\right)=\frac{y{\left(t\right)}^p}{\left(1-p\right)}{v}^{\prime }\left(t\right)$ and also obtain the value for $y\left(t\right)$.