90.15.5 problem 5

Internal problem ID [25252]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 3. Second Order Constant Coefficient Linear Differential Equations. Exercises at page 251
Problem number : 5
Date solved : Thursday, October 02, 2025 at 11:59:21 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }-8 y&=6 \,{\mathrm e}^{-4 t} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

ode:=diff(diff(y(t),t),t)+2*diff(y(t),t)-8*y(t) = 6*exp(-4*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{6 t}+c_2 -t \right ) {\mathrm e}^{-4 t} \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 32

ode=D[y[t],{t,2}]+2*D[y[t],{t,1}]-8*y[t]==6*Exp[-4*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{6} e^{-4 t} \left (-6 t+6 c_2 e^{6 t}-1+6 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.064 (sec). Leaf size: 37

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-8*y(t) + 3*Derivative(y(t), (t, 2)) - 6*exp(-4*t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- \frac {2 \sqrt {6} t}{3}} + C_{2} e^{\frac {2 \sqrt {6} t}{3}} + \frac {3 e^{- 4 t}}{20} \]