\[ y''(x)-c x^a y(x)=0 \] ✓ Mathematica : cpu = 0.0369348 (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 = 0.102 (sec), leaf count = 65
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt {x}{{\sl J}_{ \left ( a+2 \right ) ^{-1}}\left (2\,{\frac {\sqrt {-c}{x}^{a/2+1}}{a+2}}\right )}+{\it \_C2}\,\sqrt {x}{{\sl Y}_{ \left ( a+2 \right ) ^{-1}}\left (2\,{\frac {\sqrt {-c}{x}^{a/2+1}}{a+2}}\right )} \right \} \]