66.1.19 problem Problem 26

Internal problem ID [13866]
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
Date solved : Tuesday, January 28, 2025 at 06:06:10 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}+y^{2}&=4 \end{align*}

✓ Solution by Maple

Time used: 0.088 (sec). Leaf size: 31

dsolve(diff(y(x),x)^2+y(x)^2=4,y(x), singsol=all)
 

\begin{align*} y &= -2 \\ y &= 2 \\ y &= -2 \sin \left (-x +c_{1} \right ) \\ y &= 2 \sin \left (-x +c_{1} \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 3.222 (sec). Leaf size: 107

DSolve[D[y[x],x]^2+y[x]^2==4,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {2 \tan (x-c_1)}{\sqrt {\sec ^2(x-c_1)}} \\ y(x)\to \frac {2 \tan (x-c_1)}{\sqrt {\sec ^2(x-c_1)}} \\ y(x)\to -\frac {2 \tan (x+c_1)}{\sqrt {\sec ^2(x+c_1)}} \\ y(x)\to \frac {2 \tan (x+c_1)}{\sqrt {\sec ^2(x+c_1)}} \\ y(x)\to -2 \\ y(x)\to 2 \\ \end{align*}