72.5.9 problem 3 and 15(i)

Internal problem ID [14695]
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 : Tuesday, January 28, 2025 at 07:11:43 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*}

✓ Solution by Maple

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

dsolve([diff(y(t),t)=cos( y(t)),y(0) = 0],y(t), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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