2.1657 ODE No. 1657
\[ y''(x)+y(x)^3 y'(x)-y(x) y'(x) \sqrt {4 y'(x)+y(x)^4}=0 \]
✓ Mathematica : cpu = 0.64932 (sec), leaf count = 365
DSolve[y[x]^3*Derivative[1][y][x] - y[x]*Derivative[1][y][x]*Sqrt[y[x]^4 + 4*Derivative[1][y][x]] + Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to (-1)^{3/4} \sqrt {(\cosh (c_1)+\sinh (c_1)){}^2} \tan \left (\sqrt [4]{-1} x \cosh ^2(c_1) \sqrt {(\cosh (c_1)+\sinh (c_1)){}^2}+\sqrt [4]{-1} x \sinh ^2(c_1) \sqrt {(\cosh (c_1)+\sinh (c_1)){}^2}+2 \sqrt [4]{-1} x \sinh (c_1) \cosh (c_1) \sqrt {(\cosh (c_1)+\sinh (c_1)){}^2}+\sqrt [4]{-1} c_2 \cosh ^2(c_1) \sqrt {(\cosh (c_1)+\sinh (c_1)){}^2}+\sqrt [4]{-1} c_2 \sinh ^2(c_1) \sqrt {(\cosh (c_1)+\sinh (c_1)){}^2}+2 \sqrt [4]{-1} c_2 \sinh (c_1) \cosh (c_1) \sqrt {(\cosh (c_1)+\sinh (c_1)){}^2}\right )\right \},\left \{y(x)\to \sqrt [4]{-1} \sqrt {(\cosh (c_1)+\sinh (c_1)){}^2} \tan \left ((-1)^{3/4} x \cosh ^2(c_1) \sqrt {(\cosh (c_1)+\sinh (c_1)){}^2}+(-1)^{3/4} x \sinh ^2(c_1) \sqrt {(\cosh (c_1)+\sinh (c_1)){}^2}+2 (-1)^{3/4} x \sinh (c_1) \cosh (c_1) \sqrt {(\cosh (c_1)+\sinh (c_1)){}^2}+(-1)^{3/4} c_2 \cosh ^2(c_1) \sqrt {(\cosh (c_1)+\sinh (c_1)){}^2}+(-1)^{3/4} c_2 \sinh ^2(c_1) \sqrt {(\cosh (c_1)+\sinh (c_1)){}^2}+2 (-1)^{3/4} c_2 \sinh (c_1) \cosh (c_1) \sqrt {(\cosh (c_1)+\sinh (c_1)){}^2}\right )\right \}\right \}\]
✓ Maple : cpu = 0.324 (sec), leaf count = 35
dsolve(diff(diff(y(x),x),x)+y(x)^3*diff(y(x),x)-y(x)*diff(y(x),x)*(y(x)^4+4*diff(y(x),x))^(1/2)=0,y(x))
\[y \left (x \right ) = \frac {\tan \left (\left (\frac {1}{c_{1}^{2}}\right )^{{3}/{2}} \left (c_{2} +x \right )\right )}{c_{1}}\]