32.10.2 problem Exercise 35.2, page 504

Internal problem ID [5996]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 8. Special second order equations. Lesson 35. Independent variable x absent
Problem number : Exercise 35.2, page 504
Date solved : Monday, January 27, 2025 at 01:30:37 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

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

✓ Solution by Maple

Time used: 0.073 (sec). Leaf size: 46

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

\begin{align*} y \left (x \right ) &= \frac {\sqrt {c_{1} \left (\left (c_{2} +x \right )^{2} c_{1}^{2}+k \right )}}{c_{1}} \\ y \left (x \right ) &= -\frac {\sqrt {c_{1} \left (\left (c_{2} +x \right )^{2} c_{1}^{2}+k \right )}}{c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 2.961 (sec). Leaf size: 63

DSolve[y[x]^3*D[y[x],{x,2}]==k,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {k+c_1{}^2 (x+c_2){}^2}}{\sqrt {c_1}} \\ y(x)\to \frac {\sqrt {k+c_1{}^2 (x+c_2){}^2}}{\sqrt {c_1}} \\ y(x)\to \text {Indeterminate} \\ \end{align*}