73.12.25 problem 19.4 (i)

Internal problem ID [15298]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 19. Arbitrary Homogeneous linear equations with constant coefficients. Additional exercises page 369
Problem number : 19.4 (i)
Date solved : Thursday, March 13, 2025 at 05:52:07 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+16 y^{\prime }-16 y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 26

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-4*diff(diff(diff(y(x),x),x),x)+16*diff(y(x),x)-16*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_4 \,x^{2}+x c_{3} +c_{2} \right ) {\mathrm e}^{2 x}+c_{1} {\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 32

ode=D[y[x],{x,4}]-4*D[y[x],{x,3}]+16*D[y[x],x]-16*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-2 x} \left (e^{4 x} (x (c_4 x+c_3)+c_2)+c_1\right ) \]

✓ Sympy. Time used: 0.238 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-16*y(x) + 16*Derivative(y(x), x) - 4*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{4} e^{- 2 x} + \left (C_{1} + x \left (C_{2} + C_{3} x\right )\right ) e^{2 x} \]