\[ g(x) f\left (x^2+y(x)^2\right )+y(x) y'(x)+x=0 \] ✓ Mathematica : cpu = 0.359821 (sec), leaf count = 95
DSolve[x + f[x^2 + y[x]^2]*g[x] + y[x]*Derivative[1][y][x] == 0,y[x],x]
\[\text {Solve}\left [\int _1^{y(x)}\left (\frac {K[2]}{f\left (x^2+K[2]^2\right )}-\int _1^x-\frac {2 K[1] K[2] f'\left (K[1]^2+K[2]^2\right )}{f\left (K[1]^2+K[2]^2\right )^2}dK[1]\right )dK[2]+\int _1^x\left (g(K[1])+\frac {K[1]}{f\left (K[1]^2+y(x)^2\right )}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.136 (sec), leaf count = 30
dsolve(y(x)*diff(y(x),x)+f(y(x)^2+x^2)*g(x)+x = 0,y(x))
\[\int _{\textit {\_b}}^{y \left (x \right )}\frac {\textit {\_a}}{f \left (\textit {\_a}^{2}+x^{2}\right )}d \textit {\_a} +\int g \left (x \right )d x -c_{1} = 0\]