Internal problem ID [11212]
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]
\[ \boxed {{y^{\prime }}^{2}+y^{2}=1} \]
✓ Solution by Maple
Time used: 0.375 (sec). Leaf size: 29
dsolve(y(x)^2+diff(y(x),x)^2=1,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -1 y \left (x \right ) = 1 y \left (x \right ) = -\sin \left (-x +c_{1} \right ) y \left (x \right ) = \sin \left (-x +c_{1} \right ) \end{align*}
✓ Solution by Mathematica
Time used: 0.211 (sec). Leaf size: 39
DSolve[y[x]^2+(y'[x])^2==1,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*}