90.17.1 problem 1

Internal problem ID [25263]
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 : 1
Date solved : Thursday, October 02, 2025 at 11:59:27 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 35

ode:=diff(diff(diff(y(t),t),t),t)-y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{t}+c_2 \,{\mathrm e}^{-\frac {t}{2}} \sin \left (\frac {\sqrt {3}\, t}{2}\right )+c_3 \,{\mathrm e}^{-\frac {t}{2}} \cos \left (\frac {\sqrt {3}\, t}{2}\right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 52

ode=D[y[t],{t,3}]-y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-t/2} \left (c_1 e^{3 t/2}+c_2 \cos \left (\frac {\sqrt {3} t}{2}\right )+c_3 \sin \left (\frac {\sqrt {3} t}{2}\right )\right ) \end{align*}

✓ Sympy. Time used: 0.080 (sec). Leaf size: 36

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

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