71.10.2 problem 2

Internal problem ID [14426]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.3, page 210
Problem number : 2
Date solved : Monday, March 31, 2025 at 12:26:56 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

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

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 26

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

\[ y(x)\to e^x \left (c_3 e^x+c_2 \cos (x)+c_1 \sin (x)\right ) \]

✓ Sympy. Time used: 0.196 (sec). Leaf size: 20

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

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