\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -c{x}^{a}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.029004 (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 = 0.078 (sec), leaf count = 65 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt {x}{{\sl J}_{ \left ( a+ 2 \right ) ^{-1}}\left (2\,{\frac {\sqrt {-c}{x}^{a/2+1}}{a+2}}\right )}+ {\it \_C2}\,\sqrt {x}{{\sl Y}_{ \left ( a+2 \right ) ^{-1}}\left (2\,{ \frac {\sqrt {-c}{x}^{a/2+1}}{a+2}}\right )} \right \} \]