\[ \left (x^2+y(x)^2\right ) y''(x)-2 \left (x y'(x)-y(x)\right ) \left (y'(x)^2+1\right )=0 \] ✓ Mathematica : cpu = 0.359683 (sec), leaf count = 95
DSolve[-2*(-y[x] + x*Derivative[1][y][x])*(1 + Derivative[1][y][x]^2) + (x^2 + y[x]^2)*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {1}{2} \left (-\sqrt {4 x \left (-x+e^{c_2}\right )+e^{2 c_2} \cot ^2(c_1)}-e^{c_2} \cot (c_1)\right )\right \},\left \{y(x)\to \frac {1}{2} \left (\sqrt {4 x \left (-x+e^{c_2}\right )+e^{2 c_2} \cot ^2(c_1)}-e^{c_2} \cot (c_1)\right )\right \}\right \}\] ✓ Maple : cpu = 1.275 (sec), leaf count = 83
dsolve((y(x)^2+x^2)*diff(diff(y(x),x),x)-2*(diff(y(x),x)^2+1)*(x*diff(y(x),x)-y(x))=0,y(x))
\[y \left (x \right ) = \frac {c_{1}-\sqrt {c_{1}^{2}+\left (4 i c_{2} x +2\right ) c_{1}-4 c_{2}^{2} x^{2}-4 i c_{2} x +1}+1}{2 c_{2}}\]