89.12.12 problem 12

Internal problem ID [24566]
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 : 12
Date solved : Thursday, October 02, 2025 at 10:46:08 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}-16 y^{\prime \prime \prime }&=0 \end{align*}

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

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

\[ y = c_1 +c_2 x +c_3 \,x^{2}+c_4 \,{\mathrm e}^{4 x}+c_5 \,{\mathrm e}^{-4 x} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 39

ode=D[y[x],{x,5}]-16*D[y[x],{x,3}] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{64} c_1 e^{4 x}-\frac {1}{64} c_2 e^{-4 x}+x (c_5 x+c_4)+c_3 \end{align*}

✓ Sympy. Time used: 0.053 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-16*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 5)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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