solve \(\displaystyle axy''-by'+cxy=0\)

step by step

I know the solution is

\(\displaystyle y=k_1x^{u}J_{u}\left(\sqrt{\frac{c}{ a}}x\right)+k_2x^{u}Y_{u}\left(\sqrt{\frac{c}{ a}}x\right)\)

Where \(\displaystyle k_1,k_2\) are arbitrary constant, \(\displaystyle a,b,c\) are constant

\(\displaystyle u=\frac{a+b}{2a}\)

But I don't know how to derive it.