60.1.19 problem Problem 26

Internal problem ID [15147]
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 : Thursday, October 02, 2025 at 10:04:35 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.031 (sec). Leaf size: 31

ode:=diff(y(x),x)^2+y(x)^2 = 4; 
dsolve(ode,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*}

✓ Mathematica. Time used: 1.802 (sec). Leaf size: 107

ode=D[y[x],x]^2+y[x]^2==4; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 142.180 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)**2 + Derivative(y(x), x)**2 - 4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = 2 \sin {\left (C_{1} - x \right )}, \ y{\left (x \right )} = 2 \sin {\left (C_{1} + x \right )}\right ] \]