89.12.16 problem 16

Internal problem ID [24570]
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 121
Problem number : 16
Date solved : Thursday, October 02, 2025 at 10:46:10 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 27 y^{\prime \prime \prime \prime }-18 y^{\prime \prime }+8 y^{\prime }-y&=0 \end{align*}

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

ode:=27*diff(diff(diff(diff(y(x),x),x),x),x)-18*diff(diff(y(x),x),x)+8*diff(y(x),x)-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 34

ode=27*D[y[x],{x,4}]-18*D[y[x],{x,2}]+8*D[y[x],{x,1}]- y[x] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-x} \left (e^{4 x/3} (x (c_3 x+c_2)+c_1)+c_4\right ) \end{align*}

✓ Sympy. Time used: 0.132 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) + 8*Derivative(y(x), x) - 18*Derivative(y(x), (x, 2)) + 27*Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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