74.14.9 problem 9

Internal problem ID [16343]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.6, page 187
Problem number : 9
Date solved : Monday, March 31, 2025 at 02:50:44 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }+6 y^{\prime \prime }-14 y^{\prime }-104 y&=-111 \,{\mathrm e}^{t} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 28

ode:=diff(diff(diff(y(t),t),t),t)+6*diff(diff(y(t),t),t)-14*diff(y(t),t)-104*y(t) = -111*exp(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{9 t}+{\mathrm e}^{6 t}+c_2 \cos \left (t \right )+c_3 \sin \left (t \right )\right ) {\mathrm e}^{-5 t} \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 35

ode=D[ y[t],{t,3}]+6*D[y[t],{t,2}]-14*D[y[t],t]-104*y[t]==-111*Exp[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-5 t} \left (e^{6 t}+c_3 e^{9 t}+c_2 \cos (t)+c_1 \sin (t)\right ) \]

✓ Sympy. Time used: 0.248 (sec). Leaf size: 27

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-104*y(t) + 111*exp(t) - 14*Derivative(y(t), t) + 6*Derivative(y(t), (t, 2)) + Derivative(y(t), (t, 3)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{3} e^{4 t} + \left (C_{1} \sin {\left (t \right )} + C_{2} \cos {\left (t \right )}\right ) e^{- 5 t} + e^{t} \]