90.15.1 problem 1

Internal problem ID [25248]
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 : 1
Date solved : Thursday, October 02, 2025 at 11:59:19 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

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

\[ y = {\mathrm e}^{2 t} c_2 +{\mathrm e}^{-2 t} c_1 +\frac {{\mathrm e}^{-6 t}}{32} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 31

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

\begin{align*} y(t)&\to \frac {e^{-6 t}}{32}+c_1 e^{2 t}+c_2 e^{-2 t} \end{align*}

✓ Sympy. Time used: 0.061 (sec). Leaf size: 24

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

\[ y{\left (t \right )} = C_{1} e^{- 2 t} + C_{2} e^{2 t} + \frac {e^{- 6 t}}{32} \]