\[ y'(x)-\frac {y(x)-x f\left (a y(x)^2+x^2\right )}{a y(x) f\left (a y(x)^2+x^2\right )+x}=0 \] ✓ Mathematica : cpu = 0.486306 (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 = 0.497 (sec), leaf count = 52
\[\frac {\arctan \left (\frac {\sqrt {a}\, x}{\sqrt {a^{2} y \relax (x )^{2}}}\right )}{\sqrt {a}}-\frac {\left (\int _{}^{y \relax (x )^{2}+\frac {x^{2}}{a}}\frac {f \left (\textit {\_a} a \right )}{\textit {\_a}}d \textit {\_a} \right )}{2}-c_{1} = 0\]