22.2.11 problem 11

Internal problem ID [4454]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 11
Date solved : Tuesday, September 30, 2025 at 07:32:45 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+9 y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 24

ode:=diff(diff(diff(diff(diff(y(x),x),x),x),x),x)-6*diff(diff(diff(diff(y(x),x),x),x),x)+9*diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_5 x +c_4 \right ) {\mathrm e}^{3 x}+c_3 \,x^{2}+c_2 x +c_1 \]

✓ Mathematica. Time used: 0.073 (sec). Leaf size: 35

ode=D[y[x],{x,5}]-6*D[y[x],{x,4}]+9*D[y[x],{x,3}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{27} e^{3 x} (c_2 (x-1)+c_1)+x (c_5 x+c_4)+c_3 \end{align*}

✓ Sympy. Time used: 0.047 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*Derivative(y(x), (x, 3)) - 6*Derivative(y(x), (x, 4)) + Derivative(y(x), (x, 5)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x^{2} + C_{5} e^{3 x} + x \left (C_{3} + C_{4} e^{3 x}\right ) \]