Internal problem ID [5185]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 1. Introduction– Linear equations of First Order. Page 45
Problem number: 2.
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*} With initial conditions \begin {align*} [y \left (\pi \right ) = \pi ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 11
dsolve([diff(y(x),x)+cos(x)*y(x)=exp(-sin(x)),y(Pi) = Pi],y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\sin \relax (x )} x \]
✓ Solution by Mathematica
Time used: 0.223 (sec). Leaf size: 13
DSolve[{y'[x]+Cos[x]*y[x]==Exp[-Sin[x]],{y[Pi]==Pi}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x e^{-\sin (x)} \\ \end{align*}