90.17.2 problem 2

Internal problem ID [25264]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 4. Linear Constant Coefficient Differential Equations. Exercises at page 291
Problem number : 2
Date solved : Thursday, October 02, 2025 at 11:59:27 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=diff(diff(diff(y(t),t),t),t)-6*diff(diff(y(t),t),t)+12*diff(y(t),t)-8*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 23

ode=D[y[t],{t,3}]-6*D[y[t],{t,2}]+12*D[y[t],{t,1}]-8*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{2 t} (t (c_3 t+c_2)+c_1) \end{align*}

✓ Sympy. Time used: 0.112 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-8*y(t) + 12*Derivative(y(t), t) - 6*Derivative(y(t), (t, 2)) + Derivative(y(t), (t, 3)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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