60.7.1 problem 1591 (6.1)

Internal problem ID [11590]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1591 (6.1)
Date solved : Monday, January 27, 2025 at 11:23:46 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

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

✓ Solution by Maple

Time used: 0.032 (sec). Leaf size: 12

dsolve(diff(diff(y(x),x),x)-y(x)^2=0,y(x), singsol=all)
 

\[ y = 6 \operatorname {WeierstrassP}\left (x +c_{1} , 0, c_{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.728 (sec). Leaf size: 26

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

\[ y(x)\to \sqrt [3]{6} \wp \left (\frac {x+c_1}{\sqrt [3]{6}};0,c_2\right ) \]