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 : Monday, January 27, 2025 at 02:46:32 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[D[y[x],x]==2/Pi*y[x]-Sin[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

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