\[ 2 \left (x^2+1\right ) y''(x)^2+2 y'(x) \left (y'(x)+x\right )-x \left (4 y'(x)+x\right ) y''(x)-2 y(x)=0 \] ✓ Mathematica : cpu = 0.0079407 (sec), leaf count = 32
DSolve[-2*y[x] + 2*Derivative[1][y][x]*(x + Derivative[1][y][x]) - x*(x + 4*Derivative[1][y][x])*Derivative[2][y][x] + 2*(1 + x^2)*Derivative[2][y][x]^2 == 0,y[x],x]
\[\left \{\left \{y(x)\to -\frac {1}{2} \sqrt {c_2-c_1{}^2} x^2+c_1 x+c_2\right \}\right \}\] ✓ Maple : cpu = 1.013 (sec), leaf count = 59
dsolve(2*(x^2+1)*diff(diff(y(x),x),x)^2-x*diff(diff(y(x),x),x)*(x+4*diff(y(x),x))+2*(x+diff(y(x),x))*diff(y(x),x)-2*y(x)=0,y(x))
\[y \left (x \right ) = \frac {\left (c_{1}+\frac {\arcsinh \left (x \right )}{4}\right ) x \sqrt {x^{2}+1}}{2}-\frac {3 x^{2}}{16}+c_{1}^{2}+\frac {c_{1} \arcsinh \left (x \right )}{2}+\frac {\arcsinh \left (x \right )^{2}}{16}\]