\[ x y'(x) \left (a x^n+b\right )+y(x) \left (\text {a1} x^{2 n}+\text {b1} x^n+\text {c1}\right )+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.15753 (sec), leaf count = 414
\[\left \{\left \{y(x)\to 2^{\frac {1}{2} \left (\frac {\sqrt {n^2 \left (b^2-2 b-4 \text {c1}+1\right )}}{n^2}+1\right )} x^{\frac {1}{2} (-b-n+1)} e^{-\frac {\left (\sqrt {a^2-4 \text {a1}}+a\right ) x^n}{2 n}} \left (x^n\right )^{\frac {1}{2} \left (\frac {\sqrt {n^2 \left (b^2-2 b-4 \text {c1}+1\right )}}{n^2}+1\right )} \left (c_1 U\left (\frac {\left (n^2+\sqrt {\left (b^2-2 b-4 \text {c1}+1\right ) n^2}\right ) a^2+\sqrt {a^2-4 \text {a1}} n (b+n-1) a-2 \left (\sqrt {a^2-4 \text {a1}} \text {b1} n+2 \text {a1} \left (n^2+\sqrt {\left (b^2-2 b-4 \text {c1}+1\right ) n^2}\right )\right )}{2 \left (a^2-4 \text {a1}\right ) n^2},\frac {n^2+\sqrt {\left (b^2-2 b-4 \text {c1}+1\right ) n^2}}{n^2},\frac {\sqrt {a^2-4 \text {a1}} x^n}{n}\right )+c_2 L_{-\frac {-2 \left (\text {b1} n \sqrt {a^2-4 \text {a1}}+2 \text {a1} \left (\sqrt {n^2 \left (b^2-2 b-4 \text {c1}+1\right )}+n^2\right )\right )+a n \sqrt {a^2-4 \text {a1}} (b+n-1)+a^2 \left (\sqrt {n^2 \left (b^2-2 b-4 \text {c1}+1\right )}+n^2\right )}{2 n^2 \left (a^2-4 \text {a1}\right )}}^{\frac {\sqrt {n^2 \left (b^2-2 b-4 \text {c1}+1\right )}}{n^2}}\left (\frac {\sqrt {a^2-4 \text {a1}} x^n}{n}\right )\right )\right \}\right \}\]
✓ Maple : cpu = 0.176 (sec), leaf count = 148
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {a{x}^{n}}{2\,n}}}}{x}^{-{\frac {b}{2}}-{\frac {n}{2}}+{\frac {1}{2}}} \left ( {{\sl W}_{-{\frac { \left ( b+n-1 \right ) a-2\,{\it b1}}{2\,n}{\frac {1}{\sqrt {{a}^{2}-4\,{\it a1}}}}},\,{\frac {1}{2\,n}\sqrt {{b}^{2}-2\,b-4\,{\it c1}+1}}}\left ({\frac {{x}^{n}}{n}\sqrt {{a}^{2}-4\,{\it a1}}}\right )}{\it \_C2}+{{\sl M}_{-{\frac { \left ( b+n-1 \right ) a-2\,{\it b1}}{2\,n}{\frac {1}{\sqrt {{a}^{2}-4\,{\it a1}}}}},\,{\frac {1}{2\,n}\sqrt {{b}^{2}-2\,b-4\,{\it c1}+1}}}\left ({\frac {{x}^{n}}{n}\sqrt {{a}^{2}-4\,{\it a1}}}\right )}{\it \_C1} \right ) \right \} \]