Internal problem ID [5935]
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: 1(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }+{\mathrm e}^{x} y=3 \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 13
dsolve(diff(y(x),x)+exp(x)*y(x)=3*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = 3+{\mathrm e}^{-{\mathrm e}^{x}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 22
DSolve[y'[x]+Exp[x]*y[x]==3*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 3+c_1 e^{-e^x} y(x)\to 3 \end{align*}