Internal problem ID [6080]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 101. Independent variable missing. EXERCISES
Page 324
Problem number: 14.
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: 0.095 (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: 0.096 (sec). Leaf size: 20
DSolve[y[x]*y''[x]+(y'[x])^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x+c_2}{\text {ProductLog}(c_1 (x+c_2))} \\ \end{align*}