\[ y(x) \left (a x^k-(b-1) b\right )+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.05359 (sec), leaf count = 116
\[\left \{\left \{y(x)\to k^{-1/k} a^{\left .\frac {1}{2}\right /k} \left (x^k\right )^{\left .\frac {1}{2}\right /k} \left (c_1 \Gamma \left (\frac {-2 b+k+1}{k}\right ) J_{\frac {1-2 b}{k}}\left (\frac {2 \sqrt {a} \sqrt {x^k}}{k}\right )+c_2 \Gamma \left (\frac {2 b+k-1}{k}\right ) J_{\frac {2 b-1}{k}}\left (\frac {2 \sqrt {a} \sqrt {x^k}}{k}\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.102 (sec), leaf count = 67
\[ \left \{ y \left ( x \right ) =\sqrt {x} \left ( {{\sl Y}_{{\frac {1}{k}\sqrt { \left ( 2\,b-1 \right ) ^{2}}}}\left (2\,{\frac {\sqrt {a}{x}^{k/2}}{k}}\right )}{\it \_C2}+{{\sl J}_{{\frac {1}{k}\sqrt { \left ( 2\,b-1 \right ) ^{2}}}}\left (2\,{\frac {\sqrt {a}{x}^{k/2}}{k}}\right )}{\it \_C1} \right ) \right \} \]