Internal problem ID [7587]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 6.
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: 0.016 (sec). Leaf size: 15
dsolve(diff(y(x),x) + y(x)*cos(x) - sin(2*x)/2=0,y(x), singsol=all)
\[ y \relax (x ) = \sin \relax (x )-1+{\mathrm e}^{-\sin \relax (x )} c_{1} \]
✓ Solution by Mathematica
Time used: 0.089 (sec). Leaf size: 18
DSolve[y'[x] + y[x]*Cos[x] - Sin[2*x]/2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sin (x)+c_1 e^{-\sin (x)}-1 \\ \end{align*}