89.14.17 problem 17

Internal problem ID [24621]
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 : 17
Date solved : Thursday, October 02, 2025 at 10:46:32 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-4 y^{\prime \prime }-4 y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 24

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+diff(diff(diff(y(x),x),x),x)-4*diff(diff(y(x),x),x)-4*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 37

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

\begin{align*} y(x)&\to \frac {1}{2} e^{-2 x} \left (-2 c_2 e^x+c_3 e^{4 x}-c_1\right )+c_4 \end{align*}

✓ Sympy. Time used: 0.124 (sec). Leaf size: 22

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

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