67.8.15 problem 13.2 (i)

Internal problem ID [16510]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 13. Higher order equations: Extending first order concepts. Additional exercises page 259
Problem number : 13.2 (i)
Date solved : Thursday, October 02, 2025 at 01:35:50 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }&=9 \,{\mathrm e}^{-3 x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)+4*diff(y(x),x) = 9*exp(-3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {{\mathrm e}^{-4 x} c_1}{4}-3 \,{\mathrm e}^{-3 x}+c_2 \]

✓ Mathematica. Time used: 0.048 (sec). Leaf size: 26

ode=D[y[x],{x,2}]+4*D[y[x],x]==9*Exp[-3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -3 e^{-3 x}-\frac {1}{4} c_1 e^{-4 x}+c_2 \end{align*}

✓ Sympy. Time used: 0.120 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 9*exp(-3*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{- 4 x} - 3 e^{- 3 x} \]