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

✓ Solution by Maple

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

dsolve(diff(y(t),t$4)-5*diff(y(t),t$3)+6*diff(y(t),t$2)+4*diff(y(t),t)-8*y(t)=0,y(t), singsol=all)
 

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

✓ Solution by Mathematica

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

DSolve[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,y[t],t,IncludeSingularSolutions -> True]
 

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