Internal problem ID [5173]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 1.6 Introduction– Linear equations of First Order. Page 41
Problem number: 1(d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {3 y^{\prime }+y-2 \,{\mathrm e}^{-x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 17
dsolve(3*diff(y(x),x)+y(x)=2*exp(-x),y(x), singsol=all)
\[ y \relax (x ) = -{\mathrm e}^{-x}+{\mathrm e}^{-\frac {x}{3}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.064 (sec). Leaf size: 23
DSolve[3*y'[x]+y[x]==2*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} \left (-1+c_1 e^{2 x/3}\right ) \\ \end{align*}