Internal problem ID [12666]
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 (v).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-\cos \left (\frac {\pi y}{2}\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 57
dsolve(diff(y(t),t)=cos(Pi/2*y(t)),y(t), singsol=all)
\[ y \left (t \right ) = \frac {2 \arctan \left (\frac {{\mathrm e}^{c_{1} \pi +\pi t}-1}{{\mathrm e}^{c_{1} \pi +\pi t}+1}, \frac {2 \,{\mathrm e}^{\frac {1}{2} c_{1} \pi +\frac {1}{2} \pi t}}{{\mathrm e}^{c_{1} \pi +\pi t}+1}\right )}{\pi } \]
✓ Solution by Mathematica
Time used: 0.846 (sec). Leaf size: 31
DSolve[y'[t]==Cos[Pi/2*y[t]],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {2 \arcsin \left (\coth \left (\frac {1}{2} \pi (t+c_1)\right )\right )}{\pi } y(t)\to -1 y(t)\to 1 \end{align*}