Internal problem ID [7588]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }+y \cos \relax (x )-{\mathrm e}^{-\sin \relax (x )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 13
dsolve(diff(y(x),x) + y(x)*cos(x) - exp(-sin(x))=0,y(x), singsol=all)
\[ y \relax (x ) = \left (c_{1}+x \right ) {\mathrm e}^{-\sin \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.145 (sec). Leaf size: 16
DSolve[y'[x] + y[x]*Cos[x] - Exp[-Sin[x]]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (x+c_1) e^{-\sin (x)} \\ \end{align*}