\[ x y(x) y''(x)-2 x y'(x)^2+(y(x)+1) y'(x)=0 \] ✓ Mathematica : cpu = 0.0629456 (sec), leaf count = 52
DSolve[(1 + y[x])*Derivative[1][y][x] - 2*x*Derivative[1][y][x]^2 + x*y[x]*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \frac {\tan \left (\frac {1}{2} \left (\sqrt {2} \sqrt {c_1} \log (x)-\sqrt {2} \sqrt {c_1} c_2\right )\right )}{\sqrt {2} \sqrt {c_1}}\right \}\right \}\] ✓ Maple : cpu = 1.043 (sec), leaf count = 18
dsolve(x*y(x)*diff(diff(y(x),x),x)-2*x*diff(y(x),x)^2+(1+y(x))*diff(y(x),x)=0,y(x))
\[y \left (x \right ) = c_{1} \tanh \left (\frac {\ln \left (x \right )-c_{2}}{2 c_{1}}\right )\]