\[ \boxed { \left ( axy \left ( x \right ) +b{x}^{n} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +\alpha \, \left ( y \left ( x \right ) \right ) ^{3}+\beta \, \left ( y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 4.954629 (sec), leaf count = 115 \[ \text {Solve}\left [\frac {(a (-n)+a+\alpha y(x)) y(x)^{\frac {a-a n}{\beta }-1} (\alpha y(x)+\beta )^{\frac {a (n-1)}{\beta }}}{a^2 (n-1)^2 (a (n-1)+\beta )}+\frac {x^{1-n} \exp \left (-\frac {a (n-1) (\log (y(x))-\log (\alpha y(x)+\beta ))}{\beta }\right )}{a b (1-n) (n-1)}=c_1,y(x)\right ] \]
Maple: cpu = 0.156 (sec), leaf count = 202 \[ \left \{ y \left ( x \right ) ={\beta \left ( {\it RootOf} \left ( -{{\it \_Z}}^{{\frac {a \left ( n-1 \right ) }{\beta }}}{x}^{1-n}{a}^{2}\beta \,n +{\it \_C1}\,{a}^{2}b{n}^{2}-{{\it \_Z}}^{{\frac {an-a+\beta }{\beta }}} \beta \,abn+{{\it \_Z}}^{{\frac {a \left ( n-1 \right ) }{\beta }}}{x}^{1- n}{a}^{2}\beta -{{\it \_Z}}^{{\frac {a \left ( n-1 \right ) }{\beta }}}{x} ^{1-n}a{\beta }^{2}+{{\it \_Z}}^{{\frac {a \left ( n-1 \right ) }{\beta }} }a\alpha \,bn-2\,{\it \_C1}\,{a}^{2}bn+{\it \_C1}\,ab\beta \,n+{{\it \_Z }}^{{\frac {an-a+\beta }{\beta }}}\beta \,ab-{{\it \_Z}}^{{\frac {a \left ( n-1 \right ) }{\beta }}}a\alpha \,b+{{\it \_Z}}^{{\frac {a \left ( n-1 \right ) }{\beta }}}\alpha \,b\beta +{\it \_C1}\,{a}^{2}b-{ \it \_C1}\,ab\beta \right ) \beta -\alpha \right ) ^{-1}} \right \} \]