\[ \left (y(x) f\left (x^2+y(x)^2\right )-x\right ) y'(x)+x f\left (x^2+y(x)^2\right )+y(x)=0 \] ✓ Mathematica : cpu = 0.35744 (sec), leaf count = 156
\[\text {Solve}\left [\int _1^{y(x)}\left (\frac {x-f\left (x^2+K[2]^2\right ) K[2]}{x^2+K[2]^2}-\int _1^x\left (\frac {-2 K[1] K[2] f'\left (K[1]^2+K[2]^2\right )-1}{K[1]^2+K[2]^2}-\frac {2 \left (-f\left (K[1]^2+K[2]^2\right ) K[1]-K[2]\right ) K[2]}{\left (K[1]^2+K[2]^2\right )^2}\right )dK[1]\right )dK[2]+\int _1^x\frac {-f\left (K[1]^2+y(x)^2\right ) K[1]-y(x)}{K[1]^2+y(x)^2}dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.337 (sec), leaf count = 42
\[y \relax (x ) = \frac {x}{\tan \left (\RootOf \left (-2 \textit {\_Z} -\left (\int _{}^{\frac {x^{2} \left (\tan ^{2}\left (\textit {\_Z} \right )+1\right )}{\tan \left (\textit {\_Z} \right )^{2}}}\frac {f \left (\textit {\_a} \right )}{\textit {\_a}}d \textit {\_a} \right )+2 c_{1}\right )\right )}\]