30.12.28 problem 37

Internal problem ID [7620]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 4, Linear Second-Order Equations. EXERCISES 4.2 at page 164
Problem number : 37
Date solved : Tuesday, September 30, 2025 at 04:55:03 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-6 y^{\prime }+4 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 30

ode:=diff(diff(diff(y(t),t),t),t)+diff(diff(y(t),t),t)-6*diff(y(t),t)+4*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{t}+c_2 \,{\mathrm e}^{\left (\sqrt {5}-1\right ) t}+c_3 \,{\mathrm e}^{-\left (\sqrt {5}+1\right ) t} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 41

ode=D[y[t],{t,3}]+D[y[t],{t,2}]-6*D[y[t],{t,1}]+4*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to c_1 e^{-\left (\left (1+\sqrt {5}\right ) t\right )}+c_2 e^{\left (\sqrt {5}-1\right ) t}+c_3 e^t \end{align*}

✓ Sympy. Time used: 0.142 (sec). Leaf size: 31

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*y(t) - 6*Derivative(y(t), t) + Derivative(y(t), (t, 2)) + Derivative(y(t), (t, 3)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{3} e^{t} + \left (C_{1} e^{- \sqrt {5} t} + C_{2} e^{\sqrt {5} t}\right ) e^{- t} \]