\[ f\left (a y(x)^2+x^2\right ) \left (a y(x) y'(x)+x\right )-x y'(x)-y(x)=0 \] ✓ Mathematica : cpu = 0.19129 (sec), leaf count = 91
DSolve[-y[x] - x*Derivative[1][y][x] + f[x^2 + a*y[x]^2]*(x + a*y[x]*Derivative[1][y][x]) == 0,y[x],x]
\[\text {Solve}\left [\int _1^{y(x)}\left (x-a f\left (x^2+a K[2]^2\right ) K[2]-\int _1^x\left (1-2 a K[1] K[2] f'\left (K[1]^2+a K[2]^2\right )\right )dK[1]\right )dK[2]+\int _1^x\left (y(x)-f\left (K[1]^2+a y(x)^2\right ) K[1]\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.078 (sec), leaf count = 45
dsolve(f(x^2+a*y(x)^2)*(a*y(x)*diff(y(x),x)+x)-y(x)-x*diff(y(x),x) = 0,y(x))
\[-\frac {a y \left (x \right )^{2} x}{\sqrt {a^{2} y \left (x \right )^{2}}}-\left (\int _{}^{-\frac {a y \left (x \right )^{2}}{2}-\frac {x^{2}}{2}}f \left (-2 \textit {\_a} \right )d \textit {\_a} \right )+c_{1} = 0\]