14.21.5 problem 5

Internal problem ID [2714]
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 : 5
Date solved : Sunday, March 30, 2025 at 12:15:30 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=0\\ y^{\prime \prime \prime }\left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.861 (sec). Leaf size: 37

ode:=diff(diff(diff(diff(y(t),t),t),t),t)+4*diff(diff(diff(y(t),t),t),t)+14*diff(diff(y(t),t),t)-20*diff(y(t),t)+25*y(t) = 0; 
ic:=y(0) = 0, D(y)(0) = 0, (D@@2)(y)(0) = 0, (D@@3)(y)(0) = 0; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \moverset {4}{\munderset {\textit {\_a} =1}{\sum }}{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}+4 \textit {\_Z}^{3}+14 \textit {\_Z}^{2}-20 \textit {\_Z} +25, \operatorname {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 6

ode=D[y[t],{t,4}]+4*D[y[t],{t,3}]+14*D[y[t],{t,2}]-20*D[y[t],t]+25*y[t]==0; 
ic={y[0]==0,Derivative[1][y][0] ==0,Derivative[2][y][0] ==0,Derivative[3][y][0] ==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to 0 \]

✓ Sympy. Time used: 2.713 (sec). Leaf size: 3

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(25*y(t) - 20*Derivative(y(t), t) + 14*Derivative(y(t), (t, 2)) + 4*Derivative(y(t), (t, 3)) + Derivative(y(t), (t, 4)),0) 
ics = {y(0): 0, Subs(Derivative(y(t), t), t, 0): 0, Subs(Derivative(y(t), (t, 2)), t, 0): 0, Subs(Derivative(y(t), (t, 3)), t, 0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 0 \]