53.4.13 problem 14

Internal problem ID [8501]
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
Date solved : Monday, January 27, 2025 at 04:07:31 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.026 (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 &= 0 \\ y &= c_{1} \\ y &= \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: 60.109 (sec). Leaf size: 26

DSolve[y[x]*D[y[x],{x,2}]+(D[y[x],x])^3==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x+c_2}{W\left (e^{-1-c_1} (x+c_2)\right )} \]