14.21.4 problem 4

Internal problem ID [2713]
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 : 4
Date solved : Sunday, March 30, 2025 at 12:15:29 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 22

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

\[ y(t)\to c_3 e^t+c_1 \cos (t)+c_2 \sin (t) \]

✓ Sympy. Time used: 0.118 (sec). Leaf size: 17

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

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