\[ y''(x)+y(x)^3 y'(x)-y(x) y'(x) \sqrt {4 y'(x)+y(x)^4}=0 \] ✓ Mathematica : cpu = 0.351765 (sec), leaf count = 192
\[\left \{\left \{y(x)\to -\frac {i (\cosh (c_1)+\sinh (c_1)) (\cos (2 (x+c_2) (\cosh (3 c_1)+\sinh (3 c_1)))+i \sin (2 (x+c_2) (\cosh (3 c_1)+\sinh (3 c_1)))-1)}{\cos (2 (x+c_2) (\cosh (3 c_1)+\sinh (3 c_1)))+i \sin (2 (x+c_2) (\cosh (3 c_1)+\sinh (3 c_1)))+1}\right \},\left \{y(x)\to \frac {(\cosh (c_1)+\sinh (c_1)) (\cosh (2 (x+c_2) (\cosh (3 c_1)+\sinh (3 c_1)))+\sinh (2 (x+c_2) (\cosh (3 c_1)+\sinh (3 c_1)))-1)}{\cosh (2 (x+c_2) (\cosh (3 c_1)+\sinh (3 c_1)))+\sinh (2 (x+c_2) (\cosh (3 c_1)+\sinh (3 c_1)))+1}\right \}\right \}\] ✓ Maple : cpu = 1.815 (sec), leaf count = 35
\[y \relax (x ) = \frac {\tan \left (\frac {x +c_{2}}{\left (c_{1}^{2}\right )^{\frac {3}{2}}}\right )}{c_{1}}\]