\[ y(x) \left (a x^k-(b-1) b\right )+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.0379215 (sec), leaf count = 225
\[\left \{\left \{y(x)\to c_1 k^{-\frac {2 (1-b)}{k}-\frac {2 b}{k}+\frac {1}{k}} a^{\frac {1-b}{k}+\frac {1}{2} \left (\frac {2 b}{k}-\frac {1}{k}\right )} \left (x^k\right )^{\frac {1-b}{k}+\frac {1}{2} \left (\frac {2 b}{k}-\frac {1}{k}\right )} \Gamma \left (-\frac {2 b}{k}+\frac {1}{k}+1\right ) J_{\frac {1-2 b}{k}}\left (\frac {2 \sqrt {a} \sqrt {x^k}}{k}\right )+c_2 k^{-1/k} a^{\frac {b}{k}+\frac {1}{2} \left (\frac {1}{k}-\frac {2 b}{k}\right )} \left (x^k\right )^{\frac {b}{k}+\frac {1}{2} \left (\frac {1}{k}-\frac {2 b}{k}\right )} \Gamma \left (\frac {2 b}{k}-\frac {1}{k}+1\right ) J_{\frac {2 b-1}{k}}\left (\frac {2 \sqrt {a} \sqrt {x^k}}{k}\right )\right \}\right \}\] ✓ Maple : cpu = 0.194 (sec), leaf count = 67
\[ \left \{ y \left ( x \right ) =\sqrt {x} \left ( {{\sl Y}_{{\frac {1}{k}\sqrt { \left ( -1+2\,b \right ) ^{2}}}}\left (2\,{\frac {\sqrt {a}{x}^{k/2}}{k}}\right )}{\it \_C2}+{{\sl J}_{{\frac {1}{k}\sqrt { \left ( -1+2\,b \right ) ^{2}}}}\left (2\,{\frac {\sqrt {a}{x}^{k/2}}{k}}\right )}{\it \_C1} \right ) \right \} \]