Internal problem ID [6833]
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]]
\[ \boxed {y y^{\prime \prime }+{y^{\prime }}^{3}=0} \]
✓ Solution by Maple
Time used: 0.047 (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 \left (x \right ) &= 0 \\ y \left (x \right ) &= c_{1} \\ y \left (x \right ) &= \frac {x +c_{2}}{\operatorname {LambertW}\left (\left (x +c_{2} \right ) {\mathrm e}^{c_{1} -1}\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 60.095 (sec). Leaf size: 26
DSolve[y[x]*y''[x]+(y'[x])^3==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x+c_2}{W\left (e^{-1-c_1} (x+c_2)\right )} \]