89.14.9 problem 9

Internal problem ID [24613]
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 128
Problem number : 9
Date solved : Thursday, October 02, 2025 at 10:46:30 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

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

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

✓ Mathematica. Time used: 0.063 (sec). Leaf size: 39

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

\begin{align*} y(x)&\to -\frac {1}{27} c_1 e^{-3 x}+\frac {1}{8} c_2 e^{2 x}+x (c_5 x+c_4)+c_3 \end{align*}

✓ Sympy. Time used: 0.062 (sec). Leaf size: 26

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

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