87.8.4 problem 4

Internal problem ID [23358]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 65
Problem number : 4
Date solved : Thursday, October 02, 2025 at 09:39:36 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} y^{\prime \prime }+\cos \left (y\right )&=0 \end{align*}

✓ Maple. Time used: 0.067 (sec). Leaf size: 47

ode:=diff(diff(y(x),x),x)+cos(y(x)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \int _{}^{y}\frac {1}{\sqrt {-2 \sin \left (\textit {\_a} \right )+c_1}}d \textit {\_a} -x -c_2 &= 0 \\ \int _{}^{y}-\frac {1}{\sqrt {-2 \sin \left (\textit {\_a} \right )+c_1}}d \textit {\_a} -x -c_2 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 17.72 (sec). Leaf size: 81

ode=D[y[x],{x,2}]+Cos[y[x]]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} \left (\pi -4 \operatorname {JacobiAmplitude}\left (\frac {1}{2} \sqrt {(c_1-2) (x+c_2){}^2},-\frac {4}{c_1-2}\right )\right )\\ y(x)&\to \frac {1}{2} \left (\pi +4 \operatorname {JacobiAmplitude}\left (\frac {1}{2} \sqrt {(c_1-2) (x+c_2){}^2},-\frac {4}{c_1-2}\right )\right ) \end{align*}

✗ Sympy

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

Timed Out