Internal problem ID [3489]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 26
Problem number: 756.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-1+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.235 (sec). Leaf size: 29
dsolve(diff(y(x),x)^2 = 1-y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = -1 \\ y \relax (x ) = 1 \\ y \relax (x ) = -\sin \left (c_{1}-x \right ) \\ y \relax (x ) = \sin \left (c_{1}-x \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.115 (sec). Leaf size: 41
DSolve[(y'[x])^2==1-y[x]^2,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*}