53.4.5 problem 5

Internal problem ID [8493]
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 : 5
Date solved : Monday, January 27, 2025 at 04:07:21 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

\begin{align*} y^{2} y^{\prime \prime }+{y^{\prime }}^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 29

dsolve(y(x)^2*diff(y(x),x$2)+diff(y(x),x)^3=0,y(x), singsol=all)
 

\begin{align*} y &= 0 \\ y &= c_{1} \\ y &= -\frac {\operatorname {LambertW}\left (-c_{1} {\mathrm e}^{-x -c_{2}}\right )}{c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.849 (sec). Leaf size: 37

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

\[ y(x)\to c_2 \left (1+\frac {1}{\text {InverseFunction}\left [-\frac {1}{\text {$\#$1}}-\log (\text {$\#$1})+\log (\text {$\#$1}+1)\&\right ][-x+c_1]}\right ) \]