\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +a \left ( y \left ( x \right ) \right ) ^{2}-b{x}^{2\,\nu }-c{x}^{\nu -1}=0} \]
Mathematica: cpu = 0.237030 (sec), leaf count = 1835 \[ \left \{\left \{y(x)\to \frac {-2^{\frac {\nu }{2 (\nu +1)}-1} e^{-\frac {\sqrt {a} \sqrt {b} x^{\nu +1}}{\sqrt {\nu ^2+2 \nu +1}}} \nu \left (x^{\nu +1}\right )^{\frac {\nu }{2 (\nu +1)}} L_{-\frac {\frac {\sqrt {a} \sqrt {b} \nu c}{\sqrt {(\nu +1)^2}}+\frac {\sqrt {a} \sqrt {b} c}{\sqrt {(\nu +1)^2}}+b \nu }{2 (\nu b+b)}}^{\frac {\nu }{\nu +1}-1}\left (\frac {2 \sqrt {a} \sqrt {b} x^{\nu +1}}{\sqrt {\nu ^2+2 \nu +1}}\right ) x^{-\frac {\nu }{2}-1}-\frac {2^{\frac {\nu }{2 (\nu +1)}} \sqrt {a} \sqrt {b} e^{-\frac {\sqrt {a} \sqrt {b} x^{\nu +1}}{\sqrt {\nu ^2+2 \nu +1}}} (\nu +1) \left (x^{\nu +1}\right )^{\frac {\nu }{2 (\nu +1)}} L_{-\frac {\frac {\sqrt {a} \sqrt {b} \nu c}{\sqrt {(\nu +1)^2}}+\frac {\sqrt {a} \sqrt {b} c}{\sqrt {(\nu +1)^2}}+b \nu }{2 (\nu b+b)}}^{\frac {\nu }{\nu +1}-1}\left (\frac {2 \sqrt {a} \sqrt {b} x^{\nu +1}}{\sqrt {\nu ^2+2 \nu +1}}\right ) x^{\nu /2}}{\sqrt {\nu ^2+2 \nu +1}}+2^{\frac {\nu }{2 (\nu +1)}-1} e^{-\frac {\sqrt {a} \sqrt {b} x^{\nu +1}}{\sqrt {\nu ^2+2 \nu +1}}} \nu \left (x^{\nu +1}\right )^{\frac {\nu }{2 (\nu +1)}-1} L_{-\frac {\frac {\sqrt {a} \sqrt {b} \nu c}{\sqrt {(\nu +1)^2}}+\frac {\sqrt {a} \sqrt {b} c}{\sqrt {(\nu +1)^2}}+b \nu }{2 (\nu b+b)}}^{\frac {\nu }{\nu +1}-1}\left (\frac {2 \sqrt {a} \sqrt {b} x^{\nu +1}}{\sqrt {\nu ^2+2 \nu +1}}\right ) x^{\nu /2}-\frac {2^{\frac {\nu }{2 (\nu +1)}+1} \sqrt {a} \sqrt {b} e^{-\frac {\sqrt {a} \sqrt {b} x^{\nu +1}}{\sqrt {\nu ^2+2 \nu +1}}} (\nu +1) \left (x^{\nu +1}\right )^{\frac {\nu }{2 (\nu +1)}} L_{-\frac {\frac {\sqrt {a} \sqrt {b} \nu c}{\sqrt {(\nu +1)^2}}+\frac {\sqrt {a} \sqrt {b} c}{\sqrt {(\nu +1)^2}}+b \nu }{2 (\nu b+b)}-1}^{\frac {\nu }{\nu +1}}\left (\frac {2 \sqrt {a} \sqrt {b} x^{\nu +1}}{\sqrt {\nu ^2+2 \nu +1}}\right ) x^{\nu /2}}{\sqrt {\nu ^2+2 \nu +1}}+c_1 \left (-2^{\frac {\nu }{2 (\nu +1)}-1} e^{-\frac {\sqrt {a} \sqrt {b} x^{\nu +1}}{\sqrt {\nu ^2+2 \nu +1}}} \nu \left (x^{\nu +1}\right )^{\frac {\nu }{2 (\nu +1)}} U\left (\frac {\frac {\sqrt {a} \sqrt {b} \nu c}{\sqrt {(\nu +1)^2}}+\frac {\sqrt {a} \sqrt {b} c}{\sqrt {(\nu +1)^2}}+b \nu }{2 (\nu b+b)},\frac {\nu }{\nu +1},\frac {2 \sqrt {a} \sqrt {b} x^{\nu +1}}{\sqrt {\nu ^2+2 \nu +1}}\right ) x^{-\frac {\nu }{2}-1}-\frac {2^{\frac {\nu }{2 (\nu +1)}} \sqrt {a} \sqrt {b} e^{-\frac {\sqrt {a} \sqrt {b} x^{\nu +1}}{\sqrt {\nu ^2+2 \nu +1}}} (\nu +1) \left (x^{\nu +1}\right )^{\frac {\nu }{2 (\nu +1)}} U\left (\frac {\frac {\sqrt {a} \sqrt {b} \nu c}{\sqrt {(\nu +1)^2}}+\frac {\sqrt {a} \sqrt {b} c}{\sqrt {(\nu +1)^2}}+b \nu }{2 (\nu b+b)},\frac {\nu }{\nu +1},\frac {2 \sqrt {a} \sqrt {b} x^{\nu +1}}{\sqrt {\nu ^2+2 \nu +1}}\right ) x^{\nu /2}}{\sqrt {\nu ^2+2 \nu +1}}+2^{\frac {\nu }{2 (\nu +1)}-1} e^{-\frac {\sqrt {a} \sqrt {b} x^{\nu +1}}{\sqrt {\nu ^2+2 \nu +1}}} \nu \left (x^{\nu +1}\right )^{\frac {\nu }{2 (\nu +1)}-1} U\left (\frac {\frac {\sqrt {a} \sqrt {b} \nu c}{\sqrt {(\nu +1)^2}}+\frac {\sqrt {a} \sqrt {b} c}{\sqrt {(\nu +1)^2}}+b \nu }{2 (\nu b+b)},\frac {\nu }{\nu +1},\frac {2 \sqrt {a} \sqrt {b} x^{\nu +1}}{\sqrt {\nu ^2+2 \nu +1}}\right ) x^{\nu /2}-\frac {2^{\frac {\nu }{2 (\nu +1)}} \sqrt {a} \sqrt {b} e^{-\frac {\sqrt {a} \sqrt {b} x^{\nu +1}}{\sqrt {\nu ^2+2 \nu +1}}} (\nu +1) \left (\frac {\sqrt {a} \sqrt {b} \nu c}{\sqrt {(\nu +1)^2}}+\frac {\sqrt {a} \sqrt {b} c}{\sqrt {(\nu +1)^2}}+b \nu \right ) \left (x^{\nu +1}\right )^{\frac {\nu }{2 (\nu +1)}} U\left (\frac {\frac {\sqrt {a} \sqrt {b} \nu c}{\sqrt {(\nu +1)^2}}+\frac {\sqrt {a} \sqrt {b} c}{\sqrt {(\nu +1)^2}}+b \nu }{2 (\nu b+b)}+1,\frac {\nu }{\nu +1}+1,\frac {2 \sqrt {a} \sqrt {b} x^{\nu +1}}{\sqrt {\nu ^2+2 \nu +1}}\right ) x^{\nu /2}}{(\nu b+b) \sqrt {\nu ^2+2 \nu +1}}\right )}{a \left (2^{\frac {\nu }{2 (\nu +1)}} e^{-\frac {\sqrt {a} \sqrt {b} x^{\nu +1}}{\sqrt {\nu ^2+2 \nu +1}}} \left (x^{\nu +1}\right )^{\frac {\nu }{2 (\nu +1)}} c_1 U\left (\frac {\frac {\sqrt {a} \sqrt {b} \nu c}{\sqrt {(\nu +1)^2}}+\frac {\sqrt {a} \sqrt {b} c}{\sqrt {(\nu +1)^2}}+b \nu }{2 (\nu b+b)},\frac {\nu }{\nu +1},\frac {2 \sqrt {a} \sqrt {b} x^{\nu +1}}{\sqrt {\nu ^2+2 \nu +1}}\right ) x^{-\nu /2}+2^{\frac {\nu }{2 (\nu +1)}} e^{-\frac {\sqrt {a} \sqrt {b} x^{\nu +1}}{\sqrt {\nu ^2+2 \nu +1}}} \left (x^{\nu +1}\right )^{\frac {\nu }{2 (\nu +1)}} L_{-\frac {\frac {\sqrt {a} \sqrt {b} \nu c}{\sqrt {(\nu +1)^2}}+\frac {\sqrt {a} \sqrt {b} c}{\sqrt {(\nu +1)^2}}+b \nu }{2 (\nu b+b)}}^{\frac {\nu }{\nu +1}-1}\left (\frac {2 \sqrt {a} \sqrt {b} x^{\nu +1}}{\sqrt {\nu ^2+2 \nu +1}}\right ) x^{-\nu /2}\right )}\right \}\right \} \]
Maple: cpu = 0.249 (sec), leaf count = 378 \[ \left \{ y \left ( x \right ) ={\frac {1}{2\,ax} \left ( \left ( 2\, \sqrt {a}{x}^{\nu +1}{\it \_C1}\,{b}^{2}-{b}^{{\frac {3}{2}}}{\it \_C1} \,\nu +\sqrt {a}{\it \_C1}\,bc \right ) {{\sl W}_{-{\frac {c}{2\,\nu +2} \sqrt {a}{\frac {1}{\sqrt {b}}}},\,{\frac {1}{2\,\nu +2}}}\left (2\,{ \frac {\sqrt {a}\sqrt {b}{x}^{\nu +1}}{\nu +1}}\right )}+ \left ( -2\,{b}^ {3/2}{\it \_C1}\,\nu -2\,{b}^{3/2}{\it \_C1} \right ) {{\sl W}_{-{\frac {1}{2\,\nu +2} \left ( \sqrt {a}c-2\,\sqrt {b}\nu -2\,\sqrt {b} \right ) { \frac {1}{\sqrt {b}}}},\,{\frac {1}{2\,\nu +2}}}\left (2\,{\frac {\sqrt {a}\sqrt {b}{x}^{\nu +1}}{\nu +1}}\right )}+ \left ( 2\,\sqrt {a}{x}^{\nu + 1}{b}^{2}-{b}^{{\frac {3}{2}}}\nu +\sqrt {a}bc \right ) {{\sl M}_{-{ \frac {c}{2\,\nu +2}\sqrt {a}{\frac {1}{\sqrt {b}}}},\,{\frac {1}{2\, \nu +2}}}\left (2\,{\frac {\sqrt {a}\sqrt {b}{x}^{\nu +1}}{\nu +1}} \right )}+ \left ( {b}^{{\frac {3}{2}}}\nu -\sqrt {a}bc+2\,{b}^{3/2} \right ) {{\sl M}_{-{\frac {1}{2\,\nu +2} \left ( \sqrt {a}c-2\,\sqrt {b }\nu -2\,\sqrt {b} \right ) {\frac {1}{\sqrt {b}}}},\,{\frac {1}{2\,\nu + 2}}}\left (2\,{\frac {\sqrt {a}\sqrt {b}{x}^{\nu +1}}{\nu +1}}\right )} \right ) {b}^{-{\frac {3}{2}}} \left ( {{\sl W}_{-{\frac {c}{2\,\nu +2} \sqrt {a}{\frac {1}{\sqrt {b}}}},\,{\frac {1}{2\,\nu +2}}}\left (2\,{ \frac {\sqrt {a}\sqrt {b}{x}^{\nu +1}}{\nu +1}}\right )}{\it \_C1}+{ {\sl M}_{-{\frac {c}{2\,\nu +2}\sqrt {a}{\frac {1}{\sqrt {b}}}},\,{ \frac {1}{2\,\nu +2}}}\left (2\,{\frac {\sqrt {a}\sqrt {b}{x}^{\nu +1}}{ \nu +1}}\right )} \right ) ^{-1}} \right \} \]
Sage: cpu = 0.084 (sec), leaf count = 0 \[ \left [\left [\left [y\left (x\right ) = 0, {\left (b x^{2 \, \nu } + c x^{\nu - 1}\right )} a^{2} u = 0\right ]\right ], \text {\texttt {riccati}}\right ] \]