44.11.5 problem 1(e)

Internal problem ID [9275]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.3. THE METHOD OF VARIATION OF PARAMETERS. Page 71
Problem number : 1(e)
Date solved : Tuesday, September 30, 2025 at 06:15:59 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 y^{\prime \prime }+3 y^{\prime }+y&={\mathrm e}^{-3 x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

ode:=2*diff(diff(y(x),x),x)+3*diff(y(x),x)+y(x) = exp(-3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{-3 x}}{10}-2 \,{\mathrm e}^{-x} c_1 +{\mathrm e}^{-\frac {x}{2}} c_2 \]

✓ Mathematica. Time used: 0.068 (sec). Leaf size: 45

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

\begin{align*} y(x)&\to e^{-3 x}+c_1 e^{-\frac {1}{2} \left (3+\sqrt {5}\right ) x}+c_2 e^{\frac {1}{2} \left (\sqrt {5}-3\right ) x} \end{align*}

✓ Sympy. Time used: 0.140 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = C_{1} e^{- x} + C_{2} e^{- \frac {x}{2}} + \frac {e^{- 3 x}}{10} \]