68.12.23 problem 23

Internal problem ID [17617]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number : 23
Date solved : Thursday, October 02, 2025 at 02:26:19 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&=\frac {{\mathrm e}^{-3 t}}{t} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 20

ode:=diff(diff(y(t),t),t)+6*diff(y(t),t)+9*y(t) = 1/t*exp(-3*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{-3 t} \left (\ln \left (t \right ) t +t \left (c_1 -1\right )+c_2 \right ) \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 24

ode=D[y[t],{t,2}]+6*D[y[t],t]+9*y[t]==1/t*Exp[-3*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.177 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(9*y(t) + 6*Derivative(y(t), t) + Derivative(y(t), (t, 2)) - exp(-3*t)/t,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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