72.5.10 problem 3 and 15(ii)

Internal problem ID [14696]
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 : Tuesday, January 28, 2025 at 07:11:45 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*}

✓ Solution by Maple

Time used: 1.640 (sec). Leaf size: 79

dsolve([diff(y(t),t)=cos( y(t)),y(-1) = 1],y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 13

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

\[ y(t)\to \arcsin \left (\coth \left (t+1+\coth ^{-1}(\sin (1))\right )\right ) \]