89.12.3 problem 3

Internal problem ID [24557]
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 121
Problem number : 3
Date solved : Thursday, October 02, 2025 at 10:46:06 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 30

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

\begin{align*} y(x)&\to \frac {1}{4} e^{2 x} (c_2 (2 x-1)+2 c_1)+c_3 \end{align*}

✓ Sympy. Time used: 0.084 (sec). Leaf size: 14

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

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