8.21.2 problem 2

Internal problem ID [2711]
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 : 2
Date solved : Tuesday, September 30, 2025 at 05:50:06 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=diff(diff(diff(y(t),t),t),t)-6*diff(diff(y(t),t),t)+5*diff(y(t),t)+12*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-t}+c_2 \,{\mathrm e}^{3 t}+c_3 \,{\mathrm e}^{4 t} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 29

ode=D[y[t],{t,3}]-6*D[y[t],{t,2}]+5*D[y[t],t]+12*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-t} \left (e^{4 t} \left (c_3 e^t+c_2\right )+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.106 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(12*y(t) + 5*Derivative(y(t), t) - 6*Derivative(y(t), (t, 2)) + Derivative(y(t), (t, 3)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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