68.11.2 problem 14

Internal problem ID [17539]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 14
Date solved : Thursday, October 02, 2025 at 02:25:13 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=-{\mathrm e}^{-9 t} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

ode:=diff(diff(y(t),t),t)-4*diff(y(t),t)+3*y(t) = -exp(-9*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{t} c_2 +{\mathrm e}^{3 t} c_1 -\frac {{\mathrm e}^{-9 t}}{120} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 29

ode=D[y[t],{t,2}]-4*D[y[t],t]+3*y[t]==-Exp[-9*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\frac {e^{-9 t}}{120}+c_1 e^t+c_2 e^{3 t} \end{align*}

✓ Sympy. Time used: 0.135 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(3*y(t) - 4*Derivative(y(t), t) + Derivative(y(t), (t, 2)) + exp(-9*t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{t} + C_{2} e^{3 t} - \frac {e^{- 9 t}}{120} \]