76.24.12 problem 14

Internal problem ID [17740]
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 : Monday, March 31, 2025 at 04:26:19 PM
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*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

ode:=diff(diff(diff(diff(y(t),t),t),t),t)+6*diff(diff(diff(y(t),t),t),t)+9*diff(diff(y(t),t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.088 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(9*Derivative(y(t), (t, 2)) + 6*Derivative(y(t), (t, 3)) + Derivative(y(t), (t, 4)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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