\[ \left (y(x) f\left (x^2+y(x)^2\right )-x\right ) y'(x)+x f\left (x^2+y(x)^2\right )+y(x)=0 \] ✓ Mathematica : cpu = 0.349053 (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 = 0.289 (sec), leaf count = 42
\[ \left \{ y \left ( x \right ) ={x \left ( \tan \left ( {\it RootOf} \left ( -2\,{\it \_Z}-\int ^{{\frac {{x}^{2} \left ( \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+1 \right ) }{ \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}}}}\!{\frac {f \left ( {\it \_a} \right ) }{{\it \_a}}}{d{\it \_a}}+2\,{\it \_C1} \right ) \right ) \right ) ^{-1}} \right \} \]