66.16.2 problem 2

Internal problem ID [16185]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 4. Forcing and Resonance. Section 4.1 page 399
Problem number : 2
Date solved : Thursday, October 02, 2025 at 10:43:21 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=2 \,{\mathrm e}^{-3 t} \end{align*}

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

ode:=diff(diff(y(t),t),t)+6*diff(y(t),t)+8*y(t) = 2*exp(-3*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (-\frac {{\mathrm e}^{-2 t} c_1}{2}-2 \,{\mathrm e}^{-t}+c_2 \right ) {\mathrm e}^{-2 t} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 27

ode=D[y[t],{t,2}]+6*D[y[t],t]+8*y[t]==2*Exp[-3*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-4 t} \left (-2 e^t+c_2 e^{2 t}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.157 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(8*y(t) + 6*Derivative(y(t), t) + Derivative(y(t), (t, 2)) - 2*exp(-3*t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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