(a) given $$ y' = Py^2 + Qy + R. $$ If one solution say, $ U $ of that equation is known, show that the substitution $$ y = \dfrac{U + 1}{ V } $$ reduces thatequation to linear equation in terms of $V$.
(b) Given that $U= x$ is a solution to equation $$ y' = x^3 (y-x)^2 + \frac{y}{x}, $$
use the result of part (a) to find other solutions to this equation.
Well, I tried to solve part (a) and I came up with a linear equation , but the problem is in part b how to find all the other solutions to this equation?? Please help.
Your equation $V' + \big( 2 P(x) U (x) + Q(x)\big)V = - P(x)$ is correct.