\[ y'(x)-\frac {y(x)-x f\left (a y(x)^2+x^2\right )}{a y(x) f\left (a y(x)^2+x^2\right )+x}=0 \] ✓ Mathematica : cpu = 0.441786 (sec), leaf count = 184
\[\text {Solve}\left [\int _1^{y(x)}\left (\frac {-f\left (x^2+a K[2]^2\right ) K[2] a^2-x a}{x^2+a K[2]^2}-\int _1^x\left (\frac {a-2 a^2 K[1] K[2] f'\left (K[1]^2+a K[2]^2\right )}{K[1]^2+a K[2]^2}-\frac {2 a K[2] \left (a K[2]-a f\left (K[1]^2+a K[2]^2\right ) K[1]\right )}{\left (K[1]^2+a K[2]^2\right )^2}\right )dK[1]\right )dK[2]+\int _1^x\frac {a y(x)-a f\left (K[1]^2+a y(x)^2\right ) K[1]}{K[1]^2+a y(x)^2}dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.395 (sec), leaf count = 52
\[ \left \{ {\arctan \left ( {x\sqrt {a}{\frac {1}{\sqrt {{a}^{2} \left ( y \left ( x \right ) \right ) ^{2}}}}} \right ) {\frac {1}{\sqrt {a}}}}-{\frac {1}{2}\int ^{ \left ( y \left ( x \right ) \right ) ^{2}+{\frac {{x}^{2}}{a}}}\!{\frac {f \left ( {\it \_a}\,a \right ) }{{\it \_a}}}{d{\it \_a}}}-{\it \_C1}=0 \right \} \]