\[ a y'(x)+b x^{\text {a1}} y(x)+x y''(x)=0 \] ✓ Mathematica : cpu = 0.0394293 (sec), leaf count = 441
\[\left \{\left \{y(x)\to c_1 \left (\frac {1}{\text {a1}}+1\right )^{\frac {a}{\left (\frac {1}{\text {a1}}+1\right ) \text {a1}}-\frac {1}{\left (\frac {1}{\text {a1}}+1\right ) \text {a1}}} \text {a1}^{\frac {a}{\left (\frac {1}{\text {a1}}+1\right ) \text {a1}}-\frac {1}{\left (\frac {1}{\text {a1}}+1\right ) \text {a1}}} b^{\frac {1}{2} \left (\frac {1}{\left (\frac {1}{\text {a1}}+1\right ) \text {a1}}-\frac {a}{\left (\frac {1}{\text {a1}}+1\right ) \text {a1}}\right )} \left (x^{\text {a1}}\right )^{\frac {1}{2} \left (\frac {1}{\text {a1}}+1\right ) \left (\frac {1}{\left (\frac {1}{\text {a1}}+1\right ) \text {a1}}-\frac {a}{\left (\frac {1}{\text {a1}}+1\right ) \text {a1}}\right )} \Gamma \left (\frac {a}{\text {a1}+1}+\frac {\text {a1}}{\text {a1}+1}\right ) J_{\frac {a-1}{\text {a1}+1}}\left (\frac {2 \sqrt {b} \left (x^{\text {a1}}\right )^{\frac {1}{2} \left (1+\frac {1}{\text {a1}}\right )}}{\left (1+\frac {1}{\text {a1}}\right ) \text {a1}}\right )+c_2 \left (\frac {1}{\text {a1}}+1\right )^{-\frac {2 (1-a)}{\text {a1}+1}-\frac {a}{\left (\frac {1}{\text {a1}}+1\right ) \text {a1}}+\frac {1}{\left (\frac {1}{\text {a1}}+1\right ) \text {a1}}} \text {a1}^{-\frac {2 (1-a)}{\text {a1}+1}-\frac {a}{\left (\frac {1}{\text {a1}}+1\right ) \text {a1}}+\frac {1}{\left (\frac {1}{\text {a1}}+1\right ) \text {a1}}} b^{\frac {1-a}{\text {a1}+1}+\frac {1}{2} \left (\frac {a}{\left (\frac {1}{\text {a1}}+1\right ) \text {a1}}-\frac {1}{\left (\frac {1}{\text {a1}}+1\right ) \text {a1}}\right )} \left (x^{\text {a1}}\right )^{\frac {1}{2} \left (\frac {1}{\text {a1}}+1\right ) \left (\frac {a}{\left (\frac {1}{\text {a1}}+1\right ) \text {a1}}-\frac {1}{\left (\frac {1}{\text {a1}}+1\right ) \text {a1}}\right )+\frac {(1-a) \left (\frac {1}{\text {a1}}+1\right )}{\text {a1}+1}} \Gamma \left (-\frac {a}{\text {a1}+1}+\frac {\text {a1}}{\text {a1}+1}+\frac {2}{\text {a1}+1}\right ) J_{\frac {1-a}{\text {a1}+1}}\left (\frac {2 \sqrt {b} \left (x^{\text {a1}}\right )^{\frac {1}{2} \left (1+\frac {1}{\text {a1}}\right )}}{\left (1+\frac {1}{\text {a1}}\right ) \text {a1}}\right )\right \}\right \}\] ✓ Maple : cpu = 0.799 (sec), leaf count = 71
\[ \left \{ y \left ( x \right ) ={x}^{-{\frac {a}{2}}+{\frac {1}{2}}} \left ( {{\sl Y}_{{\frac {a-1}{{\it a1}+1}}}\left (2\,{\frac {\sqrt {b}{x}^{{\it a1}/2+1/2}}{{\it a1}+1}}\right )}{\it \_C2}+{{\sl J}_{{\frac {a-1}{{\it a1}+1}}}\left (2\,{\frac {\sqrt {b}{x}^{{\it a1}/2+1/2}}{{\it a1}+1}}\right )}{\it \_C1} \right ) \right \} \]