\[ y(x) \left (a x^{2 c}+b x^{c-1}\right )+y''(x)=0 \] ✓ Mathematica : cpu = 0.232644 (sec), leaf count = 225
\[\left \{\left \{y(x)\to 2^{\frac {c}{2 c+2}} x^{-c/2} \left (x^{c+1}\right )^{\frac {c}{2 c+2}} e^{-\frac {\sqrt {a} x^{c+1}}{\sqrt {-(c+1)^2}}} \left (c_1 U\left (-\frac {(c+1) \left (c b+b+\sqrt {a} c \sqrt {-(c+1)^2}\right )}{2 \sqrt {a} \left (-(c+1)^2\right )^{3/2}},\frac {c}{c+1},\frac {2 \sqrt {a} x^{c+1}}{\sqrt {-(c+1)^2}}\right )+c_2 L_{\frac {(c+1) \left (c b+b+\sqrt {a} c \sqrt {-(c+1)^2}\right )}{2 \sqrt {a} \left (-(c+1)^2\right )^{3/2}}}^{-\frac {1}{c+1}}\left (\frac {2 \sqrt {a} x^{c+1}}{\sqrt {-(c+1)^2}}\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.243 (sec), leaf count = 91
\[ \left \{ y \left ( x \right ) ={x}^{-{\frac {c}{2}}} \left ( {{\sl W}_{{\frac {-ib}{2\,c+2}{\frac {1}{\sqrt {a}}}},\, \left ( 2\,c+2 \right ) ^{-1}}\left ({\frac {2\,i{x}^{c+1}}{c+1}\sqrt {a}}\right )}{\it \_C2}+{{\sl M}_{{\frac {-ib}{2\,c+2}{\frac {1}{\sqrt {a}}}},\, \left ( 2\,c+2 \right ) ^{-1}}\left ({\frac {2\,i{x}^{c+1}}{c+1}\sqrt {a}}\right )}{\it \_C1} \right ) \right \} \]