\[ f\left (a y(x)^2+x^2\right ) \left (a y(x) y'(x)+x\right )-x y'(x)-y(x)=0 \] ✓ Mathematica : cpu = 0.264422 (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 = 0.074 (sec), leaf count = 45
\[ \left \{ -{ax \left ( y \left ( x \right ) \right ) ^{2}{\frac {1}{\sqrt {{a}^{2} \left ( y \left ( x \right ) \right ) ^{2}}}}}-\int ^{-{\frac {a \left ( y \left ( x \right ) \right ) ^{2}}{2}}-{\frac {{x}^{2}}{2}}}\!f \left ( -2\,{\it \_a} \right ) {d{\it \_a}}+{\it \_C1}=0 \right \} \]