\[ a x^{\alpha } y(x)^2+b y(x)-c x^{\beta }+x y'(x)=0 \] ✓ Mathematica : cpu = 0.271771 (sec), leaf count = 1286
\[\left \{\left \{y(x)\to \frac {x^{-\alpha } \left ((-1)^{\frac {b}{\alpha +\beta }} \sqrt {a} \alpha (\alpha +\beta )^{\frac {2 b}{\alpha +\beta }} \sqrt {c} x^{\alpha +\beta } I_{\frac {b+\beta }{\alpha +\beta }}\left (\frac {2 \sqrt {a} \sqrt {c} \sqrt {x^{\alpha +\beta }}}{\sqrt {(\alpha +\beta )^2}}\right ) c_1 \Gamma \left (\frac {b+\beta }{\alpha +\beta }\right ) \left ((\alpha +\beta )^2\right )^{\frac {\alpha }{\alpha +\beta }}+(-1)^{\frac {b}{\alpha +\beta }} \sqrt {a} \beta (\alpha +\beta )^{\frac {2 b}{\alpha +\beta }} \sqrt {c} x^{\alpha +\beta } I_{\frac {b+\beta }{\alpha +\beta }}\left (\frac {2 \sqrt {a} \sqrt {c} \sqrt {x^{\alpha +\beta }}}{\sqrt {(\alpha +\beta )^2}}\right ) c_1 \Gamma \left (\frac {b+\beta }{\alpha +\beta }\right ) \left ((\alpha +\beta )^2\right )^{\frac {\alpha }{\alpha +\beta }}+(-1)^{\frac {b}{\alpha +\beta }} \sqrt {a} \alpha (\alpha +\beta )^{\frac {2 b}{\alpha +\beta }} \sqrt {c} x^{\alpha +\beta } I_{\frac {b-\alpha }{\alpha +\beta }-1}\left (\frac {2 \sqrt {a} \sqrt {c} \sqrt {x^{\alpha +\beta }}}{\sqrt {(\alpha +\beta )^2}}\right ) c_1 \Gamma \left (\frac {b+\beta }{\alpha +\beta }\right ) \left ((\alpha +\beta )^2\right )^{\frac {\alpha }{\alpha +\beta }}+(-1)^{\frac {b}{\alpha +\beta }} \sqrt {a} \beta (\alpha +\beta )^{\frac {2 b}{\alpha +\beta }} \sqrt {c} x^{\alpha +\beta } I_{\frac {b-\alpha }{\alpha +\beta }-1}\left (\frac {2 \sqrt {a} \sqrt {c} \sqrt {x^{\alpha +\beta }}}{\sqrt {(\alpha +\beta )^2}}\right ) c_1 \Gamma \left (\frac {b+\beta }{\alpha +\beta }\right ) \left ((\alpha +\beta )^2\right )^{\frac {\alpha }{\alpha +\beta }}+(-1)^{\frac {\alpha }{\alpha +\beta }} \sqrt {a} (\alpha +\beta )^{\frac {2 \alpha }{\alpha +\beta }+1} \sqrt {c} x^{\alpha +\beta } I_{-\frac {b+\beta }{\alpha +\beta }}\left (\frac {2 \sqrt {a} \sqrt {c} \sqrt {x^{\alpha +\beta }}}{\sqrt {(\alpha +\beta )^2}}\right ) \Gamma \left (\frac {2 \alpha -b+\beta }{\alpha +\beta }\right ) \left ((\alpha +\beta )^2\right )^{\frac {b}{\alpha +\beta }}+(-1)^{\frac {\alpha }{\alpha +\beta }} \sqrt {a} \alpha (\alpha +\beta )^{\frac {2 \alpha }{\alpha +\beta }} \sqrt {c} x^{\alpha +\beta } I_{\frac {\alpha -b}{\alpha +\beta }+1}\left (\frac {2 \sqrt {a} \sqrt {c} \sqrt {x^{\alpha +\beta }}}{\sqrt {(\alpha +\beta )^2}}\right ) \Gamma \left (\frac {2 \alpha -b+\beta }{\alpha +\beta }\right ) \left ((\alpha +\beta )^2\right )^{\frac {b}{\alpha +\beta }}+(-1)^{\frac {\alpha }{\alpha +\beta }} \sqrt {a} \beta (\alpha +\beta )^{\frac {2 \alpha }{\alpha +\beta }} \sqrt {c} x^{\alpha +\beta } I_{\frac {\alpha -b}{\alpha +\beta }+1}\left (\frac {2 \sqrt {a} \sqrt {c} \sqrt {x^{\alpha +\beta }}}{\sqrt {(\alpha +\beta )^2}}\right ) \Gamma \left (\frac {2 \alpha -b+\beta }{\alpha +\beta }\right ) \left ((\alpha +\beta )^2\right )^{\frac {b}{\alpha +\beta }}+(-1)^{\frac {b}{\alpha +\beta }} \alpha (\alpha +\beta )^{\frac {2 b}{\alpha +\beta }} \sqrt {x^{\alpha +\beta }} I_{\frac {b-\alpha }{\alpha +\beta }}\left (\frac {2 \sqrt {a} \sqrt {c} \sqrt {x^{\alpha +\beta }}}{\sqrt {(\alpha +\beta )^2}}\right ) c_1 \Gamma \left (\frac {b+\beta }{\alpha +\beta }\right ) \left ((\alpha +\beta )^2\right )^{\frac {\alpha }{\alpha +\beta }+\frac {1}{2}}+(-1)^{\frac {b}{\alpha +\beta }+1} b (\alpha +\beta )^{\frac {2 b}{\alpha +\beta }} \sqrt {x^{\alpha +\beta }} I_{\frac {b-\alpha }{\alpha +\beta }}\left (\frac {2 \sqrt {a} \sqrt {c} \sqrt {x^{\alpha +\beta }}}{\sqrt {(\alpha +\beta )^2}}\right ) c_1 \Gamma \left (\frac {b+\beta }{\alpha +\beta }\right ) \left ((\alpha +\beta )^2\right )^{\frac {\alpha }{\alpha +\beta }+\frac {1}{2}}+(-1)^{\frac {\alpha }{\alpha +\beta }} (\alpha -b) (\alpha +\beta )^{\frac {2 \alpha }{\alpha +\beta }} \sqrt {x^{\alpha +\beta }} I_{\frac {\alpha -b}{\alpha +\beta }}\left (\frac {2 \sqrt {a} \sqrt {c} \sqrt {x^{\alpha +\beta }}}{\sqrt {(\alpha +\beta )^2}}\right ) \Gamma \left (\frac {2 \alpha -b+\beta }{\alpha +\beta }\right ) \left ((\alpha +\beta )^2\right )^{\frac {b}{\alpha +\beta }+\frac {1}{2}}\right )}{2 a \sqrt {(\alpha +\beta )^2} \sqrt {x^{\alpha +\beta }} \left ((-1)^{\frac {b}{\alpha +\beta }} (\alpha +\beta )^{\frac {2 b}{\alpha +\beta }} I_{\frac {b-\alpha }{\alpha +\beta }}\left (\frac {2 \sqrt {a} \sqrt {c} \sqrt {x^{\alpha +\beta }}}{\sqrt {(\alpha +\beta )^2}}\right ) c_1 \Gamma \left (\frac {b+\beta }{\alpha +\beta }\right ) \left ((\alpha +\beta )^2\right )^{\frac {\alpha }{\alpha +\beta }}+(-1)^{\frac {\alpha }{\alpha +\beta }} (\alpha +\beta )^{\frac {2 \alpha }{\alpha +\beta }} I_{\frac {\alpha -b}{\alpha +\beta }}\left (\frac {2 \sqrt {a} \sqrt {c} \sqrt {x^{\alpha +\beta }}}{\sqrt {(\alpha +\beta )^2}}\right ) \Gamma \left (\frac {2 \alpha -b+\beta }{\alpha +\beta }\right ) \left ((\alpha +\beta )^2\right )^{\frac {b}{\alpha +\beta }}\right )}\right \}\right \}\]
✓ Maple : cpu = 0.294 (sec), leaf count = 174
\[ \left \{ y \left ( x \right ) =-{\frac {{x}^{1-\alpha }}{ax} \left ( {{\sl Y}_{{\frac {b+\beta }{\alpha +\beta }}}\left (2\,{\frac {\sqrt {-ac}{x}^{\alpha /2+\beta /2}}{\alpha +\beta }}\right )}{\it \_C1}+{{\sl J}_{{\frac {b+\beta }{\alpha +\beta }}}\left (2\,{\frac {\sqrt {-ac}{x}^{\alpha /2+\beta /2}}{\alpha +\beta }}\right )} \right ) {x}^{{\frac {\alpha }{2}}+{\frac {\beta }{2}}}\sqrt {-ac} \left ( {{\sl Y}_{{\frac {b-\alpha }{\alpha +\beta }}}\left (2\,{\frac {\sqrt {-ac}{x}^{\alpha /2+\beta /2}}{\alpha +\beta }}\right )}{\it \_C1}+{{\sl J}_{{\frac {b-\alpha }{\alpha +\beta }}}\left (2\,{\frac {\sqrt {-ac}{x}^{\alpha /2+\beta /2}}{\alpha +\beta }}\right )} \right ) ^{-1}} \right \} \]