72.3.4 problem 4

Internal problem ID [14597]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.4 page 61
Problem number : 4
Date solved : Monday, March 31, 2025 at 12:39:39 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.753 (sec). Leaf size: 54

ode:=diff(y(t),t) = sin(y(t)); 
ic:=y(0) = 1; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \arctan \left (\frac {\sin \left (1\right )}{-\cos \left (1\right ) \sinh \left (t \right )+\cosh \left (t \right )}, \frac {\left (1-\cos \left (1\right )\right ) {\mathrm e}^{2 t}-\cos \left (1\right )-1}{\left (-1+\cos \left (1\right )\right ) {\mathrm e}^{2 t}-\cos \left (1\right )-1}\right ) \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 16

ode=D[y[t],t]==Sin[y[t]]; 
ic={y[0]==1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \arccos (-\tanh (t-\text {arctanh}(\cos (1)))) \]

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-sin(y(t)) + Derivative(y(t), t),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out