78.6.3 problem 2.b

Internal problem ID [21066]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 7, Nonlinear systems. Problems section 7.11
Problem number : 2.b
Date solved : Thursday, October 02, 2025 at 07:02:02 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 45

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

\[ y = \arctan \left (\frac {{\mathrm e}^{2 x} c_1^{2}-1}{{\mathrm e}^{2 x} c_1^{2}+1}, \frac {2 \,{\mathrm e}^{x} c_1}{{\mathrm e}^{2 x} c_1^{2}+1}\right ) \]

✓ Mathematica. Time used: 0.432 (sec). Leaf size: 35

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

\begin{align*} y(x)&\to 2 \arctan \left (\tanh \left (\frac {x+c_1}{2}\right )\right )\\ y(x)&\to -\frac {\pi }{2}\\ y(x)&\to \frac {\pi }{2} \end{align*}

✗ Sympy

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

Timed Out