11.1.4 problem 9

Internal problem ID [1465]
Book : Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima, Meade
Section : Chapter 4.1, Higher order linear differential equations. General theory. page 173
Problem number : 9
Date solved : Saturday, March 29, 2025 at 10:55:52 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&=0 \end{align*}

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

ode:=diff(diff(diff(y(t),t),t),t)+2*diff(diff(y(t),t),t)-diff(y(t),t)-2*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (c_2 \,{\mathrm e}^{3 t}+c_3 \,{\mathrm e}^{t}+c_1 \right ) {\mathrm e}^{-2 t} \]

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

ode=D[ y[t],{t,3}]+2*D[y[t],{t,2}]-D[y[t],t]-2*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-2 t} \left (c_2 e^t+c_3 e^{3 t}+c_1\right ) \]

✓ Sympy. Time used: 0.157 (sec). Leaf size: 19

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

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