72.5.32 problem 37 (i)

Internal problem ID [14718]
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 : 37 (i)
Date solved : Tuesday, January 28, 2025 at 07:12:33 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y \cos \left (\frac {\pi y}{2}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 22

dsolve(diff(y(t),t)=y(t)*cos(Pi/2*y(t)),y(t), singsol=all)
 

\[ t -\int _{}^{y}\frac {\sec \left (\frac {\textit {\_a} \pi }{2}\right )}{\textit {\_a}}d \textit {\_a} +c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.297 (sec). Leaf size: 47

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

\begin{align*} y(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {\sec \left (\frac {1}{2} \pi K[1]\right )}{K[1]}dK[1]\&\right ][t+c_1] \\ y(t)\to -1 \\ y(t)\to 0 \\ y(t)\to 1 \\ \end{align*}