74.13.8 problem 25

Internal problem ID [16295]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.5, page 175
Problem number : 25
Date solved : Thursday, March 13, 2025 at 08:10:07 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime }+2 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 32

ode:=diff(diff(diff(y(t),t),t),t)-5*diff(y(t),t)+2*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_{1} {\mathrm e}^{2 t}+c_{2} {\mathrm e}^{\left (\sqrt {2}-1\right ) t}+c_{3} {\mathrm e}^{-\left (1+\sqrt {2}\right ) t} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 43

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

\[ y(t)\to c_1 e^{-\left (\left (1+\sqrt {2}\right ) t\right )}+c_2 e^{\left (\sqrt {2}-1\right ) t}+c_3 e^{2 t} \]

✓ Sympy. Time used: 0.201 (sec). Leaf size: 32

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

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