Internal problem ID [2700]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (\cos \relax (x )+1\right ) y^{\prime }-\sin \relax (x ) \left (\sin \relax (x )+\sin \relax (x ) \cos \relax (x )-y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \relax (x ) = \left (x -\sin \relax (x )+c_{1}\right ) \left (1+\cos \relax (x )\right ) \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 24
DSolve[(1+Cos[x])*y'[x]==Sin[x]*( Sin[x]+Sin[x]*Cos[x]-y[x] ),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \cos ^2\left (\frac {x}{2}\right ) (2 x-2 \sin (x)+c_1) \\ \end{align*}