73.3.24 problem 4.6 (d)

Internal problem ID [14987]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.6 (d)
Date solved : Monday, March 31, 2025 at 01:10:20 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 46

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

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

✓ Mathematica. Time used: 0.281 (sec). Leaf size: 44

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

\begin{align*} y(x)\to -\arccos (-\tanh (x+c_1)) \\ y(x)\to \arccos (-\tanh (x+c_1)) \\ y(x)\to 0 \\ y(x)\to -\pi \\ y(x)\to \pi \\ \end{align*}

✗ Sympy

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

Timed Out