\[ y''(x)-c x^a y(x)=0 \] ✓ Mathematica : cpu = 0.0229783 (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 = 0.231 (sec), leaf count = 63
\[\left \{y \left (x \right ) = \left (c_{1} \BesselJ \left (\frac {1}{a +2}, \frac {2 \sqrt {-c}\, x^{\frac {a}{2}+1}}{a +2}\right )+c_{2} \BesselY \left (\frac {1}{a +2}, \frac {2 \sqrt {-c}\, x^{\frac {a}{2}+1}}{a +2}\right )\right ) \sqrt {x}\right \}\]