Internal problem ID [10188]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IV, differential equations of the first order and higher degree than the first. Article
24. Equations solvable for \(p\). Page 49
Problem number: Ex 3.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}+y^{2}-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
dsolve(y(x)^2+diff(y(x),x)^2=1,y(x), singsol=all)
\begin{align*} y \relax (x ) = -1 \\ y \relax (x ) = 1 \\ y \relax (x ) = -\sin \left (-x +c_{1}\right ) \\ y \relax (x ) = \sin \left (-x +c_{1}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.099 (sec). Leaf size: 41
DSolve[y[x]^2+(y'[x])^2==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sin (x-c_1) \\ y(x)\to \sin (x+c_1) \\ y(x)\to -1 \\ y(x)\to 1 \\ y(x)\to \text {Interval}[\{-1,1\}] \\ \end{align*}