\[ y''(x)-c x^a y(x)=0 \] ✓ Mathematica : cpu = 0.0231569 (sec), leaf count = 170
\[\left \{\left \{y(x)\to (a+2)^{-\frac {1}{a+2}} c_1 c^{\frac {1}{2 (a+2)}} x^{\frac {\frac {a}{2}+1}{a+2}} \Gamma \left (1-\frac {1}{a+2}\right ) I_{-\frac {1}{a+2}}\left (\frac {2 \sqrt {c} x^{\frac {a+2}{2}}}{a+2}\right )+(-1)^{\frac {1}{a+2}} (a+2)^{-\frac {1}{a+2}} c_2 c^{\frac {1}{2 (a+2)}} x^{1-\frac {\frac {a}{2}+1}{a+2}} \Gamma \left (1+\frac {1}{a+2}\right ) I_{\frac {1}{a+2}}\left (\frac {2 \sqrt {c} x^{\frac {a+2}{2}}}{a+2}\right )\right \}\right \}\] ✓ Maple : cpu = 1.077 (sec), leaf count = 63
\[ \left \{ y \left ( x \right ) =\sqrt {x} \left ( {{\sl Y}_{ \left ( a+2 \right ) ^{-1}}\left (2\,{\frac {\sqrt {-c}{x}^{a/2+1}}{a+2}}\right )}{\it \_C2}+{{\sl J}_{ \left ( a+2 \right ) ^{-1}}\left (2\,{\frac {\sqrt {-c}{x}^{a/2+1}}{a+2}}\right )}{\it \_C1} \right ) \right \} \]