14.21.3 problem 3

Internal problem ID [2712]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.15, Higher order equations. Excercises page 263
Problem number : 3
Date solved : Sunday, March 30, 2025 at 12:15:28 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }-8 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 26

ode:=diff(diff(diff(diff(y(t),t),t),t),t)-5*diff(diff(diff(y(t),t),t),t)+6*diff(diff(y(t),t),t)+4*diff(y(t),t)-8*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{-t} \left (\left (c_4 \,t^{2}+c_3 t +c_2 \right ) {\mathrm e}^{3 t}+c_1 \right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 32

ode=D[y[t],{t,4}]-5*D[y[t],{t,3}]+6*D[y[t],{t,2}]+4*D[y[t],t]-8*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-t} \left (e^{3 t} (t (c_4 t+c_3)+c_2)+c_1\right ) \]

✓ Sympy. Time used: 0.228 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-8*y(t) + 4*Derivative(y(t), t) + 6*Derivative(y(t), (t, 2)) - 5*Derivative(y(t), (t, 3)) + Derivative(y(t), (t, 4)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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