30.12.32 problem 41

Internal problem ID [7624]
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 : 41
Date solved : Tuesday, September 30, 2025 at 04:55:05 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y^{\prime }-12 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=diff(diff(diff(y(t),t),t),t)+3*diff(diff(y(t),t),t)-4*diff(y(t),t)-12*y(t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (c_2 \,{\mathrm e}^{5 t}+c_3 \,{\mathrm e}^{t}+c_1 \right ) {\mathrm e}^{-3 t} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 28

ode=D[y[t],{t,3}]+3*D[y[t],{t,2}]-4*D[y[t],{t,1}]-12*y[t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-3 t} \left (c_2 e^t+c_3 e^{5 t}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.113 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-12*y(t) - 4*Derivative(y(t), t) + 3*Derivative(y(t), (t, 2)) + Derivative(y(t), (t, 3)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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