\[ y''(x)+y(x)^3 y'(x)-y(x) y'(x) \sqrt {4 y'(x)+y(x)^4}=0 \] ✓ Mathematica : cpu = 0.298539 (sec), leaf count = 192
\[\left \{\left \{y(x)\to -\frac {i (\sinh (c_1)+\cosh (c_1)) (\cos (2 (c_2+x) (\sinh (3 c_1)+\cosh (3 c_1)))+i \sin (2 (c_2+x) (\sinh (3 c_1)+\cosh (3 c_1)))-1)}{\cos (2 (c_2+x) (\sinh (3 c_1)+\cosh (3 c_1)))+i \sin (2 (c_2+x) (\sinh (3 c_1)+\cosh (3 c_1)))+1}\right \},\left \{y(x)\to \frac {(\sinh (c_1)+\cosh (c_1)) (\cosh (2 (c_2+x) (\sinh (3 c_1)+\cosh (3 c_1)))+\sinh (2 (c_2+x) (\sinh (3 c_1)+\cosh (3 c_1)))-1)}{\cosh (2 (c_2+x) (\sinh (3 c_1)+\cosh (3 c_1)))+\sinh (2 (c_2+x) (\sinh (3 c_1)+\cosh (3 c_1)))+1}\right \}\right \}\] ✓ Maple : cpu = 0.193 (sec), leaf count = 35
\[ \left \{ y \left ( x \right ) ={\frac {1}{{\it \_C1}}\tan \left ( \left ( {{\it \_C1}}^{-2} \right ) ^{{\frac {3}{2}}} \left ( {\it \_C2}+x \right ) \right ) },y \left ( x \right ) ={\frac {1}{{\it \_C1}}\tanh \left ( \left ( {{\it \_C1}}^{-2} \right ) ^{{\frac {3}{2}}} \left ( {\it \_C2}+x \right ) \right ) } \right \} \]