\[ a y'(x)+b x^{\text {a1}} y(x)+x y''(x)=0 \] ✓ Mathematica : cpu = 0.0525812 (sec), leaf count = 165
\[\left \{\left \{y(x)\to \left (\frac {1}{\text {a1}}+1\right )^{\frac {a-1}{\text {a1}+1}} \text {a1}^{\frac {a-1}{\text {a1}+1}} b^{\frac {1-a}{2 \text {a1}+2}} \left (x^{\text {a1}}\right )^{-\frac {a-1}{2 \text {a1}}} \left (c_2 \Gamma \left (\frac {-a+\text {a1}+2}{\text {a1}+1}\right ) J_{\frac {1-a}{\text {a1}+1}}\left (\frac {2 \sqrt {b} \left (x^{\text {a1}}\right )^{\frac {\text {a1}+1}{2 \text {a1}}}}{\text {a1}+1}\right )+c_1 \Gamma \left (\frac {a+\text {a1}}{\text {a1}+1}\right ) J_{\frac {a-1}{\text {a1}+1}}\left (\frac {2 \sqrt {b} \left (x^{\text {a1}}\right )^{\frac {\text {a1}+1}{2 \text {a1}}}}{\text {a1}+1}\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.081 (sec), leaf count = 71
\[ \left \{ y \left ( x \right ) ={x}^{-{\frac {a}{2}}+{\frac {1}{2}}} \left ( {{\sl J}_{{\frac {a-1}{{\it a1}+1}}}\left (2\,{\frac {\sqrt {b}{x}^{{\it a1}/2+1/2}}{{\it a1}+1}}\right )}{\it \_C1}+{{\sl Y}_{{\frac {a-1}{{\it a1}+1}}}\left (2\,{\frac {\sqrt {b}{x}^{{\it a1}/2+1/2}}{{\it a1}+1}}\right )}{\it \_C2} \right ) \right \} \]