\[ y''(x)-c x^a y(x)=0 \] ✓ Mathematica : cpu = 0.0191805 (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 = 0.117 (sec), leaf count = 63
\[y \relax (x ) = \sqrt {x}\, \left (\BesselY \left (\frac {1}{a +2}, \frac {2 \sqrt {-c}\, x^{\frac {a}{2}+1}}{a +2}\right ) c_{2}+\BesselJ \left (\frac {1}{a +2}, \frac {2 \sqrt {-c}\, x^{\frac {a}{2}+1}}{a +2}\right ) c_{1}\right )\]