\[ -f(x) g\left (x^a y(x)\right )+a y(x)+x y'(x)=0 \] ✓ Mathematica : cpu = 3.19309 (sec), leaf count = 41
\[\text {Solve}\left [\int _1^{x^a y(x)}\frac {1}{g(K[1])}dK[1]=\int _1^xf(K[2]) K[2]^{a-1}dK[2]+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.21 (sec), leaf count = 33
\[ \left \{ y \left ( x \right ) ={\frac {{\it RootOf} \left ( -\int \!{x}^{a-1}f \left ( x \right ) \,{\rm d}x+\int ^{{\it \_Z}}\! \left ( g \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) }{{x}^{a}}} \right \} \]