28.1.134 problem 157

Internal problem ID [4440]
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 : 157
Date solved : Monday, January 27, 2025 at 09:17:27 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 )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 32

dsolve((1+cos(x))*diff(y(x),x)+sin(x)*(sin(x)+sin(x)*cos(x)-y(x))=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-2 \sin \left (x \right )^{3}+3 \cos \left (x \right ) \sin \left (x \right )+6 c_{1} -3 x}{6 \cos \left (x \right )+6} \]

✓ Solution by Mathematica

Time used: 0.100 (sec). Leaf size: 39

DSolve[(1+Cos[x])*D[y[x],x] + Sin[x]*(Sin[x]+Sin[x]*Cos[x]-y[x])==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{24} \sec ^2\left (\frac {x}{2}\right ) (-6 x-3 \sin (x)+3 \sin (2 x)+\sin (3 x)+24 c_1) \]