Internal problem ID [6641]
Book: Second order enumerated odes
Section: section 1
Problem number: 8.
ODE order: 2.
ODE degree: 2.
CAS Maple gives this as type [[_2nd_order, _quadrature]]
Solve \begin {gather*} \boxed {\left (y^{\prime \prime }\right )^{2}-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)^2=1,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{2} x^{2}+c_{1} x +c_{2} \\ y \relax (x ) = -\frac {1}{2} x^{2}+c_{1} x +c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 37
DSolve[(y''[x])^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*}