72.5.9 problem 3 and 15(i)

Internal problem ID [14616]
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 1.6 page 89
Problem number : 3 and 15(i)
Date solved : Thursday, March 13, 2025 at 04:09:12 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.142 (sec). Leaf size: 32

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

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

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 8

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

\[ y(t)\to \arcsin (\tanh (t)) \]

✗ Sympy

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

Timed Out