58.1.8 problem 8

Internal problem ID [9079]
Book : Second order enumerated odes
Section : section 1
Problem number : 8
Date solved : Monday, January 27, 2025 at 05:32:06 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} {y^{\prime \prime }}^{2}&=1 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)^2=1,y(x), singsol=all)
 

\begin{align*} y &= \frac {1}{2} x^{2}+c_{1} x +c_{2} \\ y &= -\frac {1}{2} x^{2}+c_{1} x +c_{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 37

DSolve[(D[y[x],{x,2}])^2==1,y[x],x,IncludeSingularSolutions -> True]
 

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