\[ a x^k-(b-1) b+x^2 \left (y'(x)+y(x)^2\right )=0 \] ✓ Mathematica : cpu = 0.133718 (sec), leaf count = 397
\[\left \{\left \{y(x)\to \frac {-\sqrt {a} c_1 x^k \Gamma \left (\frac {-2 b+k+1}{k}\right ) J_{\frac {-2 b+k+1}{k}}\left (\frac {2 \sqrt {a} \sqrt {x^k}}{k}\right )+\sqrt {a} c_1 x^k \Gamma \left (\frac {-2 b+k+1}{k}\right ) J_{-\frac {2 b+k-1}{k}}\left (\frac {2 \sqrt {a} \sqrt {x^k}}{k}\right )+c_1 \sqrt {x^k} \Gamma \left (\frac {-2 b+k+1}{k}\right ) J_{\frac {1-2 b}{k}}\left (\frac {2 \sqrt {a} \sqrt {x^k}}{k}\right )+\sqrt {a} x^k \Gamma \left (\frac {2 b+k-1}{k}\right ) J_{-\frac {-2 b+k+1}{k}}\left (\frac {2 \sqrt {a} \sqrt {x^k}}{k}\right )-\sqrt {a} x^k \Gamma \left (\frac {2 b+k-1}{k}\right ) J_{\frac {2 b+k-1}{k}}\left (\frac {2 \sqrt {a} \sqrt {x^k}}{k}\right )+\sqrt {x^k} \Gamma \left (\frac {2 b+k-1}{k}\right ) J_{\frac {2 b-1}{k}}\left (\frac {2 \sqrt {a} \sqrt {x^k}}{k}\right )}{2 x \sqrt {x^k} \left (c_1 \Gamma \left (\frac {-2 b+k+1}{k}\right ) J_{\frac {1-2 b}{k}}\left (\frac {2 \sqrt {a} \sqrt {x^k}}{k}\right )+\Gamma \left (\frac {2 b+k-1}{k}\right ) J_{\frac {2 b-1}{k}}\left (\frac {2 \sqrt {a} \sqrt {x^k}}{k}\right )\right )}\right \}\right \}\]
✓ Maple : cpu = 0.154 (sec), leaf count = 219
\[ \left \{ y \left ( x \right ) ={\frac {1}{2\,x} \left ( -2\,{{\sl J}_{{\frac {\sqrt { \left ( -1+2\,b \right ) ^{2}}+k}{k}}}\left (2\,{\frac {\sqrt {a}{x}^{k/2}}{k}}\right )}\sqrt {a}{x}^{k/2}-2\,\sqrt {a}{x}^{k/2}{{\sl Y}_{{\frac {\sqrt { \left ( -1+2\,b \right ) ^{2}}+k}{k}}}\left (2\,{\frac {\sqrt {a}{x}^{k/2}}{k}}\right )}{\it \_C1}+2\, \left ( {{\sl Y}_{{\frac {\sqrt { \left ( -1+2\,b \right ) ^{2}}}{k}}}\left (2\,{\frac {\sqrt {a}{x}^{k/2}}{k}}\right )}{\it \_C1}+{{\sl J}_{{\frac {\sqrt { \left ( -1+2\,b \right ) ^{2}}}{k}}}\left (2\,{\frac {\sqrt {a}{x}^{k/2}}{k}}\right )} \right ) \left ( 1/2+ \left ( b-1/2 \right ) {\it csgn} \left ( -1+2\,b \right ) \right ) \right ) \left ( {{\sl Y}_{{\frac {1}{k}\sqrt { \left ( -1+2\,b \right ) ^{2}}}}\left (2\,{\frac {\sqrt {a}{x}^{k/2}}{k}}\right )}{\it \_C1}+{{\sl J}_{{\frac {1}{k}\sqrt { \left ( -1+2\,b \right ) ^{2}}}}\left (2\,{\frac {\sqrt {a}{x}^{k/2}}{k}}\right )} \right ) ^{-1}} \right \} \]