\[ -f(x) g\left (x^a y(x)\right )+a y(x)+x y'(x)=0 \] ✓ Mathematica : cpu = 3.40912 (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 = 0.279 (sec), leaf count = 33
\[\left \{y \left (x \right ) = x^{-a} \RootOf \left (c_{1}+\int _{}^{\textit {\_Z}}\frac {1}{g \left (\textit {\_a} \right )}d \textit {\_a} -\left (\int x^{a -1} f \left (x \right )d x \right )\right )\right \}\]