28.1.64 problem 65

Internal problem ID [4370]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 65
Date solved : Monday, January 27, 2025 at 09:09:24 AM
CAS classification : [_linear]

\begin{align*} \left (1+\cos \left (x \right )\right ) y^{\prime }&=\sin \left (x \right ) \left (\sin \left (x \right )+\sin \left (x \right ) \cos \left (x \right )-y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 16

dsolve((1+cos(x))*diff(y(x),x)=sin(x)*( sin(x)+sin(x)*cos(x)-y(x) ),y(x), singsol=all)
 

\[ y \left (x \right ) = \left (-\sin \left (x \right )+x +c_{1} \right ) \left (\cos \left (x \right )+1\right ) \]

✓ Solution by Mathematica

Time used: 0.086 (sec). Leaf size: 24

DSolve[(1+Cos[x])*D[y[x],x]==Sin[x]*( Sin[x]+Sin[x]*Cos[x]-y[x] ),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cos ^2\left (\frac {x}{2}\right ) (2 x-2 \sin (x)+c_1) \]