Internal problem ID [4150]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\frac {3 k y^{2}}{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.037 (sec). Leaf size: 15
dsolve(diff(y(x),x$2)=3/2*k*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {4 \WeierstrassP \left (c_{1}+x , 0, c_{2}\right )}{k} \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 36
DSolve[y''[x]==3/2*(k*y[x]^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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}} \\ \end{align*}