Assume $x(t)$ be the solution to the differential equation $x''+a(t)x'+b(t)x=0$ where $a,b$ are continuous functions.
I need to show that $y$ is a second and linear independent solution of the equation such that $y(t)=x(t)u(t)$ and $u(t)$ is a non constant solution to $u''+(2(x'/x)+a)u'=0$.
So far I have used the substitution that $v=u'$ and create a first order linear equation to solve. However, what method is most appropriate to solve $u'$? I was thinking separation by variables.
Any help thanks :)