67.4.23 problem 5.3 (c)

Internal problem ID [16392]
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 : Thursday, October 02, 2025 at 01:27:32 PM
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*}

✓ Maple. Time used: 0.034 (sec). Leaf size: 11

ode:=diff(y(x),x)+5*y(x) = exp(-3*x); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \sinh \left (x \right ) {\mathrm e}^{-4 x} \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 21

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

\begin{align*} y(x)&\to \frac {1}{2} e^{-5 x} \left (e^{2 x}-1\right ) \end{align*}

✓ Sympy. Time used: 0.100 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*y(x) + Derivative(y(x), x) - exp(-3*x),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (\frac {1}{2} - \frac {e^{- 2 x}}{2}\right ) e^{- 3 x} \]