73.4.23 problem 5.3 (c)

Internal problem ID [15105]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page 103
Problem number : 5.3 (c)
Date solved : Tuesday, January 28, 2025 at 07:30:54 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+5 y&={\mathrm e}^{-3 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 16

dsolve([diff(y(x),x)+5*y(x)=exp(-3*x),y(0) = 0],y(x), singsol=all)
 

\[ y = \frac {\left ({\mathrm e}^{2 x}-1\right ) {\mathrm e}^{-5 x}}{2} \]

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 21

DSolve[{D[y[x],x]+5*y[x]==Exp[-3*x],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{-5 x} \left (e^{2 x}-1\right ) \]