90.15.3 problem 3

Internal problem ID [25250]
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 : 3
Date solved : Thursday, October 02, 2025 at 11:59:20 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{-2 t} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

ode:=diff(diff(y(t),t),t)+5*diff(y(t),t)+6*y(t) = exp(-2*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{-3 t} \left (\left (c_1 +t \right ) {\mathrm e}^{t}+c_2 \right ) \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 23

ode=D[y[t],{t,2}]+5*D[y[t],{t,1}]+6*y[t]==Exp[-2*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-3 t} \left (e^t (t-1+c_2)+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.051 (sec). Leaf size: 20

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

\[ y{\left (t \right )} = C_{1} \sin {\left (t \right )} + C_{2} \cos {\left (t \right )} + \frac {e^{- 2 t}}{30} \]