Internal problem ID [12130]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 26.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{2}+y^{2}=4} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 31
dsolve(diff(y(x),x)^2+y(x)^2=4,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -2 \\ y \left (x \right ) &= 2 \\ y \left (x \right ) &= -2 \sin \left (c_{1} -x \right ) \\ y \left (x \right ) &= 2 \sin \left (c_{1} -x \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.306 (sec). Leaf size: 43
DSolve[y'[x]^2+y[x]^2==4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 \cos (x+c_1) \\ y(x)\to 2 \cos (x-c_1) \\ y(x)\to -2 \\ y(x)\to 2 \\ y(x)\to \text {Interval}[\{-2,2\}] \\ \end{align*}