89.11.7 problem 7

Internal problem ID [24532]
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 117
Problem number : 7
Date solved : Thursday, October 02, 2025 at 10:45:56 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

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

\[ y = \left (c_1 \,{\mathrm e}^{4 x}+c_2 \,{\mathrm e}^{3 x}+c_3 \right ) {\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 28

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

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

✓ Sympy. Time used: 0.097 (sec). Leaf size: 20

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

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