73.12.5 problem 19.1 (e)

Internal problem ID [15278]
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 : 19.1 (e)
Date solved : Thursday, March 13, 2025 at 05:51:54 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-18 y^{\prime \prime }+81 y&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 25

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-18*diff(diff(y(x),x),x)+81*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 35

ode=D[y[x],{x,4}]-18*D[y[x],{x,2}]+81*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-3 x} \left (c_3 e^{6 x}+x \left (c_4 e^{6 x}+c_2\right )+c_1\right ) \]

✓ Sympy. Time used: 0.103 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(81*y(x) - 18*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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