20.3.24 problem Problem 31

Internal problem ID [3633]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential Equations. page 59
Problem number : Problem 31
Date solved : Monday, January 27, 2025 at 07:48:00 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&={\mathrm e}^{-2 x} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

dsolve(diff(y(x),x)+y(x)=exp(-2*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \left (-{\mathrm e}^{-x}+c_{1} \right ) {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.058 (sec). Leaf size: 19

DSolve[D[y[x],x]+y[x]==Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (-1+c_1 e^x\right ) \]