68.14.21 problem 21

Internal problem ID [17713]
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 : 21
Date solved : Thursday, October 02, 2025 at 02:27:17 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-10 y^{\prime }-24 y&={\mathrm e}^{-3 t} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 30

ode:=diff(diff(diff(y(t),t),t),t)+3*diff(diff(y(t),t),t)-10*diff(y(t),t)-24*y(t) = exp(-3*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {\left (6 c_3 \,{\mathrm e}^{7 t}+6 c_2 \,{\mathrm e}^{2 t}+{\mathrm e}^{t}+6 c_1 \right ) {\mathrm e}^{-4 t}}{6} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 40

ode=D[ y[t],{t,3}]+3*D[y[t],{t,2}]-10*D[y[t],t]-24*y[t]==Exp[-3*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {1}{6} e^{-4 t} \left (e^t+6 c_2 e^{2 t}+6 c_3 e^{7 t}+6 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.174 (sec). Leaf size: 31

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-24*y(t) - 10*Derivative(y(t), t) + 3*Derivative(y(t), (t, 2)) + Derivative(y(t), (t, 3)) - exp(-3*t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- 4 t} + C_{2} e^{- 2 t} + C_{3} e^{3 t} + \frac {e^{- 3 t}}{6} \]