Chapter 2.6, Problem 47E

To determine

a)

To show:

The substitution $y=u+\frac{1}{v}$ reduces the equation $\frac{dy}{dx}=P\left(x\right)y^2+Q\left(x\right)y+R\left(x\right)$ to a linear equation in $v$.

To determine

(b)

To find:

The solution of the equation $\frac{dy}{dx}=x^3{\left(y-x\right)}^2+\frac{y}{x}$.