66.5.38 problem 37 (vii)

Internal problem ID [16011]
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 (vii)
Date solved : Thursday, October 02, 2025 at 10:38:39 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 22

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

\[ t -\int _{}^{y}\frac {\csc \left (\frac {\pi \textit {\_a}}{2}\right )}{\textit {\_a}}d \textit {\_a} +c_1 = 0 \]

✓ Mathematica. Time used: 0.138 (sec). Leaf size: 37

ode=D[y[t],t]==y[t]*Sin[Pi/2*y[t]]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.244 (sec). Leaf size: 15

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

\[ \int \limits ^{y{\left (t \right )}} \frac {1}{y \sin {\left (\frac {y \pi }{2} \right )}}\, dy = C_{1} + t \]