72.5.36 problem 37 (v)

Internal problem ID [14651]
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)
Date solved : Monday, March 31, 2025 at 12:49:57 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.012 (sec). Leaf size: 24

ode:=diff(y(t),t) = cos(1/2*Pi*y(t)); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {2 \arctan \left (\tanh \left (\frac {\pi \left (c_1 +t \right )}{2}\right ), \operatorname {sech}\left (\frac {\pi \left (c_1 +t \right )}{2}\right )\right )}{\pi } \]

✓ Mathematica. Time used: 0.458 (sec). Leaf size: 31

ode=D[y[t],t]==Cos[Pi/2*y[t]]; 
ic={}; 
DSolve[{ode,ic},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*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-cos(pi*y(t)/2) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out