89.14.22 problem 22

Internal problem ID [24626]
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 : 22
Date solved : Thursday, October 02, 2025 at 10:46:34 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}+y^{\prime \prime \prime \prime }-9 y^{\prime \prime \prime }-13 y^{\prime \prime }+8 y^{\prime }+12 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 30

ode:=diff(diff(diff(diff(diff(y(x),x),x),x),x),x)+diff(diff(diff(diff(y(x),x),x),x),x)-9*diff(diff(diff(y(x),x),x),x)-13*diff(diff(y(x),x),x)+8*diff(y(x),x)+12*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_2 \,{\mathrm e}^{5 x}+c_3 \,{\mathrm e}^{3 x}+c_1 \,{\mathrm e}^{x}+c_5 x +c_4 \right ) {\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 40

ode=D[y[x],{x,5}]+D[y[x],{x,4}]-9*D[y[x],{x,3}]-13*D[y[x],{x,2}]+8*D[y[x],{x,1}]+12*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-2 x} \left (c_2 x+c_3 e^x+c_4 e^{3 x}+c_5 e^{5 x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.142 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(12*y(x) + 8*Derivative(y(x), x) - 13*Derivative(y(x), (x, 2)) - 9*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)) + Derivative(y(x), (x, 5)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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