76.24.12 problem 14

Internal problem ID [17811]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 6. Systems of First Order Linear Equations. Section 6.2 (Basic Theory of First Order Linear Systems). Problems at page 398
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 11:03:18 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(diff(y(t),t$4)+6*diff(y(t),t$3)+9*diff(y(t),t$2)=0,y(t), singsol=all)
 

\[ y = \left (t c_4 +c_{3} \right ) {\mathrm e}^{-3 t}+c_{2} t +c_{1} \]

✓ Solution by Mathematica

Time used: 0.065 (sec). Leaf size: 34

DSolve[D[y[t],{t,4}]+6*D[y[t],{t,3}]+9*D[y[t],{t,2}]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{27} e^{-3 t} (c_2 (3 t+2)+3 c_1)+c_4 t+c_3 \]