89.14.4 problem 4

Internal problem ID [24608]
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 : 4
Date solved : Thursday, October 02, 2025 at 10:46:28 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 27

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-5*diff(diff(diff(y(x),x),x),x)+5*diff(diff(y(x),x),x)+5*diff(y(x),x)-6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 36

ode=D[y[x],{x,4}]-5*D[y[x],{x,3}]+5*D[y[x],{x,2}]+5*D[y[x],{x,1}]-6*y[x] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.128 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*y(x) + 5*Derivative(y(x), x) + 5*Derivative(y(x), (x, 2)) - 4*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{x} + C_{2} e^{\frac {x \left (1 - \sqrt {97}\right )}{8}} + C_{3} e^{\frac {x \left (1 + \sqrt {97}\right )}{8}} \]