12.17 problem Ex 18

Internal problem ID [10173]

Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 19. Summary. Page 29
Problem number: Ex 18.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {y^{\prime }+y \cos \relax (x )-\frac {\sin \left (2 x \right )}{2}=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 15

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

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

Solution by Mathematica

Time used: 0.06 (sec). Leaf size: 18

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

\begin{align*} y(x)\to \sin (x)+c_1 e^{-\sin (x)}-1 \\ \end{align*}