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 : Monday, January 27, 2025 at 06:12:13 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*}

✓ Solution by Maple

Time used: 1.034 (sec). Leaf size: 37

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

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

✓ Solution by Mathematica

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

DSolve[{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,{y[0]==0,Derivative[1][y][0] ==0,Derivative[2][y][0] ==0,Derivative[3][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 0 \]