Internal problem ID [4037]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous
Methods
Problem number: Exercise 12.24, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }+\cos \relax (x ) y-{\mathrm e}^{-\sin \relax (x )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve(diff(y(x),x)+y(x)*cos(x)=exp(-sin(x)),y(x), singsol=all)
\[ y \relax (x ) = \left (x +c_{1}\right ) {\mathrm e}^{-\sin \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.198 (sec). Leaf size: 16
DSolve[y'[x]+y[x]*Cos[x]==Exp[-Sin[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (x+c_1) e^{-\sin (x)} \\ \end{align*}