31.1.17 problem 6.4

Internal problem ID [5715]
Book : Differential Equations, By George Boole F.R.S. 1865
Section : Chapter 2
Problem number : 6.4
Date solved : Monday, January 27, 2025 at 01:11:16 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+y \cos \left (x \right )&=\frac {\sin \left (2 x \right )}{2} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

dsolve(diff(y(x),x)+y(x)*cos(x)=1/2*sin(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.052 (sec). Leaf size: 18

DSolve[D[y[x],x]+y[x]*Cos[x]==1/2*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sin (x)+c_1 e^{-\sin (x)}-1 \]