89.12.19 problem 19

Internal problem ID [24573]
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 : 19
Date solved : Thursday, October 02, 2025 at 10:46:10 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }-6 y^{\prime }-2 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 36

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-5*diff(diff(y(x),x),x)-6*diff(y(x),x)-2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_4 \,{\mathrm e}^{-\left (\sqrt {3}-1\right ) x}+c_3 \,{\mathrm e}^{\left (1+\sqrt {3}\right ) x}+{\mathrm e}^{-x} \left (c_2 x +c_1 \right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 47

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

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

✓ Sympy. Time used: 0.147 (sec). Leaf size: 34

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

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