Internal problem ID [6683]
Book: Second order enumerated odes
Section: section 1
Problem number: 50.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]
Solve \begin {gather*} \boxed {y y^{\prime \prime }+\left (y^{\prime }\right )^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 27
dsolve(y(x)*diff(y(x),x$2)+diff(y(x),x)^3=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = c_{1} \\ y \relax (x ) = {\mathrm e}^{\LambertW \left (\left (c_{2}+x \right ) {\mathrm e}^{c_{1}} {\mathrm e}^{-1}\right )-c_{1}+1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.149 (sec). Leaf size: 25
DSolve[y[x]*y''[x]+y'[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{\text {ProductLog}\left (e^{-1-c_1} (x+c_2)\right )+1+c_1} \\ \end{align*}