\[ f\left (a y(x)^2+x^2\right ) \left (a y(x) y'(x)+x\right )-x y'(x)-y(x)=0 \] ✓ Mathematica : cpu = 0.303217 (sec), leaf count = 91
\[\text {Solve}\left [\int _1^{y(x)}\left (x-a f\left (x^2+a K[2]^2\right ) K[2]-\int _1^x\left (1-2 a K[1] K[2] f'\left (K[1]^2+a K[2]^2\right )\right )dK[1]\right )dK[2]+\int _1^x\left (y(x)-f\left (K[1]^2+a y(x)^2\right ) K[1]\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.126 (sec), leaf count = 45
\[-\frac {a y \relax (x )^{2} x}{\sqrt {a^{2} y \relax (x )^{2}}}-\left (\int _{}^{-\frac {a y \relax (x )^{2}}{2}-\frac {x^{2}}{2}}f \left (-2 \textit {\_a} \right )d \textit {\_a} \right )+c_{1} = 0\]