44.4.47 problem 31

Internal problem ID [7060]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.1 Solution curves without a solution. Exercises 2.1 at page 44
Problem number : 31
Date solved : Wednesday, March 05, 2025 at 04:04:49 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

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

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

✓ Mathematica. Time used: 0.964 (sec). Leaf size: 36

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

\[ y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{\pi \sin (K[1])-2 K[1]}dK[1]\&\right ]\left [-\frac {x}{\pi }+c_1\right ] \]

✓ Sympy. Time used: 0.718 (sec). Leaf size: 19

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

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