32.10.8 problem Exercise 35.8, page 504

Internal problem ID [6002]
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 35.8, page 504
Date solved : Monday, January 27, 2025 at 01:31:56 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} y^{\prime \prime }&=\frac {3 k y^{2}}{2} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

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

\[ y = \frac {4 \operatorname {WeierstrassP}\left (x +c_1 , 0, c_2\right )}{k} \]

✓ Solution by Mathematica

Time used: 1.458 (sec). Leaf size: 36

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

\[ y(x)\to \frac {2^{2/3} \wp \left (\frac {\sqrt [3]{k} (x+c_1)}{2^{2/3}};0,c_2\right )}{\sqrt [3]{k}} \]