Internal problem ID [12662]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-y \cos \left (\frac {\pi y}{2}\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(t),t)=y(t)*cos(Pi/2*y(t)),y(t), singsol=all)
\[ t -\left (\int _{}^{y \left (t \right )}\frac {1}{\textit {\_a} \cos \left (\frac {\pi \textit {\_a}}{2}\right )}d \textit {\_a} \right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 4.801 (sec). Leaf size: 47
DSolve[y'[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*}