89.14.2 problem 2

Internal problem ID [24606]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 8. Linear Differential Equations with constant coefficients. Exercises at page 128
Problem number : 2
Date solved : Thursday, October 02, 2025 at 10:46:28 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

ode:=diff(diff(diff(y(x),x),x),x)+4*diff(diff(y(x),x),x)+5*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.102 (sec). Leaf size: 39

ode=D[y[x],{x,3}]+4*D[y[x],{x,2}]+5*D[y[x],{x,1}] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{5} e^{-2 x} ((c_2-2 c_1) \sin (x)-(c_1+2 c_2) \cos (x))+c_3 \end{align*}

✓ Sympy. Time used: 0.111 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*Derivative(y(x), x) + 4*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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