74.12.24 problem 24

Internal problem ID [16252]
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 : 24
Date solved : Thursday, March 13, 2025 at 08:07:21 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+9 y&={\mathrm e}^{-3 t} \ln \left (t \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 30

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

\[ y = \frac {{\mathrm e}^{-3 t} \left (2 \ln \left (t \right ) t^{2}+4 c_{1} t -3 t^{2}+4 c_{2} \right )}{4} \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 36

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

\[ y(t)\to \frac {1}{4} e^{-3 t} \left (-3 t^2+2 t^2 \log (t)+4 c_2 t+4 c_1\right ) \]

✓ Sympy. Time used: 0.303 (sec). Leaf size: 24

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)*log(t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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