Internal problem ID [3997]
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]
\[ \boxed {{y^{\prime }}^{2}+y^{2}=1} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
dsolve(diff(y(x),x)^2 = 1-y(x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -1 y \left (x \right ) = 1 y \left (x \right ) = -\sin \left (c_{1} -x \right ) y \left (x \right ) = \sin \left (c_{1} -x \right ) \end{align*}
✓ Solution by Mathematica
Time used: 0.203 (sec). Leaf size: 39
DSolve[(y'[x])^2==1-y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \cos (x+c_1) y(x)\to \cos (x-c_1) y(x)\to -1 y(x)\to 1 y(x)\to \text {Interval}[\{-1,1\}] \end{align*}