Internal problem ID [11202]
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]
\[ \boxed {y^{2}+{y^{\prime }}^{2}=1} \]
✓ Solution by Maple
Time used: 0.078 (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 (c_{1} -x \right ) \\ y \left (x \right ) &= \sin \left (c_{1} -x \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*}