\[ a y(x)^2-b y(x)-c x^{\beta }+x y'(x)=0 \] ✓ Mathematica : cpu = 0.134711 (sec), leaf count = 244
DSolve[-(c*x^beta) - b*y[x] + a*y[x]^2 + x*Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to -\frac {\sqrt {-a} \sqrt {c} x^{\beta /2} \left (-2 \operatorname {BesselJ}\left (\frac {b}{\beta }-1,\frac {2 \sqrt {-a} \sqrt {c} x^{\beta /2}}{\beta }\right )+c_1 \operatorname {BesselJ}\left (1-\frac {b}{\beta },\frac {2 \sqrt {-a} \sqrt {c} x^{\beta /2}}{\beta }\right )-c_1 \operatorname {BesselJ}\left (-\frac {b+\beta }{\beta },\frac {2 \sqrt {-a} \sqrt {c} x^{\beta /2}}{\beta }\right )\right )-b c_1 \operatorname {BesselJ}\left (-\frac {b}{\beta },\frac {2 \sqrt {-a} \sqrt {c} x^{\beta /2}}{\beta }\right )}{2 a \left (\operatorname {BesselJ}\left (\frac {b}{\beta },\frac {2 \sqrt {-a} \sqrt {c} x^{\beta /2}}{\beta }\right )+c_1 \operatorname {BesselJ}\left (-\frac {b}{\beta },\frac {2 \sqrt {-a} \sqrt {c} x^{\beta /2}}{\beta }\right )\right )}\right \}\right \}\] ✓ Maple : cpu = 0.079 (sec), leaf count = 171
dsolve(x*diff(y(x),x)+a*y(x)^2-b*y(x)-c*x^beta = 0,y(x))
\[y \left (x \right ) = \frac {-\sqrt {-a c}\, \left (\operatorname {BesselY}\left (\frac {b +\beta }{\beta }, \frac {2 \sqrt {-a c}\, x^{\frac {\beta }{2}}}{\beta }\right ) c_{1}+\operatorname {BesselJ}\left (\frac {b +\beta }{\beta }, \frac {2 \sqrt {-a c}\, x^{\frac {\beta }{2}}}{\beta }\right )\right ) x^{\frac {\beta }{2}}+b \left (\operatorname {BesselY}\left (\frac {b}{\beta }, \frac {2 \sqrt {-a c}\, x^{\frac {\beta }{2}}}{\beta }\right ) c_{1}+\operatorname {BesselJ}\left (\frac {b}{\beta }, \frac {2 \sqrt {-a c}\, x^{\frac {\beta }{2}}}{\beta }\right )\right )}{a \left (\operatorname {BesselY}\left (\frac {b}{\beta }, \frac {2 \sqrt {-a c}\, x^{\frac {\beta }{2}}}{\beta }\right ) c_{1}+\operatorname {BesselJ}\left (\frac {b}{\beta }, \frac {2 \sqrt {-a c}\, x^{\frac {\beta }{2}}}{\beta }\right )\right )}\]