66.5.10 problem 3 and 15(ii)

Internal problem ID [15983]
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(ii)
Date solved : Thursday, October 02, 2025 at 10:36:05 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.595 (sec). Leaf size: 65

ode:=diff(y(t),t) = cos(y(t)); 
ic:=[y(-1) = 1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 13

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

\begin{align*} y(t)&\to \arcsin \left (\coth \left (t+1+\coth ^{-1}(\sin (1))\right )\right ) \end{align*}

✗ Sympy

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

Timed Out