72.5.11 problem 3 and 15(iii)

Internal problem ID [14697]
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(iii)
Date solved : Tuesday, January 28, 2025 at 07:11:49 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=-\frac {\pi }{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 7

dsolve([diff(y(t),t)=cos( y(t)),y(0) = -1/2*Pi],y(t), singsol=all)
 

\[ y = -\frac {\pi }{2} \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 10

DSolve[{D[y[t],t]==Cos[ y[t]],{y[0]==-Pi/2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {\pi }{2} \]