\[ x y'(x) \left (a x^n+b\right )+y(x) \left (\text {a1} x^{2 n}+\text {b1} x^n+\text {c1}\right )+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.108877 (sec), leaf count = 664
\[\left \{\left \{y(x)\to c_1 x^{\frac {1-n}{2}} 2^{\frac {\sqrt {b^2 n^2-2 b n^2-4 \text {c1} n^2+n^2}+n^2}{2 n^2}} \left (x^n\right )^{\frac {\sqrt {b^2 n^2-2 b n^2-4 \text {c1} n^2+n^2}+n^2}{2 n^2}} \exp \left (\frac {1}{2} \left (-\frac {a x^n}{n}-b \log (x)\right )-\frac {\sqrt {a^2-4 \text {a1}} x^n}{2 n}\right ) U\left (\frac {\frac {\sqrt {\left (b^2-2 b-4 \text {c1}+1\right ) n^2} a^2}{n^2}+a^2+\sqrt {a^2-4 \text {a1}} a+\frac {\sqrt {a^2-4 \text {a1}} b a}{n}-\frac {\sqrt {a^2-4 \text {a1}} a}{n}-4 \text {a1}-\frac {4 \text {a1} \sqrt {\left (b^2-2 b-4 \text {c1}+1\right ) n^2}}{n^2}-\frac {2 \sqrt {a^2-4 \text {a1}} \text {b1}}{n}}{2 \left (a^2-4 \text {a1}\right )},\frac {n^2+\sqrt {b^2 n^2-2 b n^2-4 \text {c1} n^2+n^2}}{n^2},\frac {\sqrt {a^2-4 \text {a1}} x^n}{n}\right )+c_2 x^{\frac {1-n}{2}} 2^{\frac {\sqrt {b^2 n^2-2 b n^2-4 \text {c1} n^2+n^2}+n^2}{2 n^2}} \left (x^n\right )^{\frac {\sqrt {b^2 n^2-2 b n^2-4 \text {c1} n^2+n^2}+n^2}{2 n^2}} \exp \left (\frac {1}{2} \left (-\frac {a x^n}{n}-b \log (x)\right )-\frac {\sqrt {a^2-4 \text {a1}} x^n}{2 n}\right ) L_{-\frac {\frac {\sqrt {\left (b^2-2 b-4 \text {c1}+1\right ) n^2} a^2}{n^2}+a^2+\sqrt {a^2-4 \text {a1}} a+\frac {\sqrt {a^2-4 \text {a1}} b a}{n}-\frac {\sqrt {a^2-4 \text {a1}} a}{n}-4 \text {a1}-\frac {4 \text {a1} \sqrt {\left (b^2-2 b-4 \text {c1}+1\right ) n^2}}{n^2}-\frac {2 \sqrt {a^2-4 \text {a1}} \text {b1}}{n}}{2 \left (a^2-4 \text {a1}\right )}}^{\frac {n^2+\sqrt {b^2 n^2-2 b n^2-4 \text {c1} n^2+n^2}}{n^2}-1}\left (\frac {\sqrt {a^2-4 \text {a1}} x^n}{n}\right )\right \}\right \}\] ✓ Maple : cpu = 0.175 (sec), leaf count = 148
\[y \relax (x ) = x^{-\frac {b}{2}-\frac {n}{2}+\frac {1}{2}} {\mathrm e}^{-\frac {a \,x^{n}}{2 n}} \left (\WhittakerW \left (-\frac {\left (b +n -1\right ) a -2 \mathit {b1}}{2 \sqrt {a^{2}-4 \mathit {a1}}\, n}, \frac {\sqrt {b^{2}-2 b -4 \mathit {c1} +1}}{2 n}, \frac {\sqrt {a^{2}-4 \mathit {a1}}\, x^{n}}{n}\right ) c_{2}+\WhittakerM \left (-\frac {\left (b +n -1\right ) a -2 \mathit {b1}}{2 \sqrt {a^{2}-4 \mathit {a1}}\, n}, \frac {\sqrt {b^{2}-2 b -4 \mathit {c1} +1}}{2 n}, \frac {\sqrt {a^{2}-4 \mathit {a1}}\, x^{n}}{n}\right ) c_{1}\right )\]