81.3.7 problem 7

Internal problem ID [18625]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 12:04:35 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)+cos(x)*y(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: 0.043 (sec). Leaf size: 18

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

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