89.14.23 problem 23

Internal problem ID [24627]
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 : 23
Date solved : Thursday, October 02, 2025 at 10:46:34 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-11 y^{\prime \prime \prime }+36 y^{\prime \prime }-16 y^{\prime }-64 y&=0 \end{align*}

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

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-11*diff(diff(diff(y(x),x),x),x)+36*diff(diff(y(x),x),x)-16*diff(y(x),x)-64*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 32

ode=D[y[x],{x,4}]-11*D[y[x],{x,3}]+36*D[y[x],{x,2}]-16*D[y[x],{x,1}]-64*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.150 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-64*y(x) - 16*Derivative(y(x), x) + 36*Derivative(y(x), (x, 2)) - 11*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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