81.14.4 problem 18-14

Internal problem ID [21689]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 18. Algebra of differential operators. Page 435
Problem number : 18-14
Date solved : Thursday, October 02, 2025 at 08:00:01 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+12 y^{\prime \prime \prime }+54 y^{\prime \prime }+108 y^{\prime }+81 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+12*diff(diff(diff(y(x),x),x),x)+54*diff(diff(y(x),x),x)+108*diff(y(x),x)+81*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 28

ode=D[y[x],{x,4}]+12*D[y[x],{x,3}]+54*D[y[x],{x,2}]+108*D[y[x],x]+81*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.118 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(81*y(x) + 108*Derivative(y(x), x) + 54*Derivative(y(x), (x, 2)) + 12*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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