71.10.3 problem 3

Internal problem ID [14419]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.3, page 210
Problem number : 3
Date solved : Saturday, February 22, 2025 at 03:47:43 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-16 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 29

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

\[ y = {\mathrm e}^{2 x} c_{1} +c_{2} {\mathrm e}^{-2 x}+c_{3} \sin \left (2 x \right )+c_4 \cos \left (2 x \right ) \]

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

ode=D[y[x],{x,4}]-16*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 e^{2 x}+c_3 e^{-2 x}+c_2 \cos (2 x)+c_4 \sin (2 x) \]

✓ Sympy. Time used: 0.081 (sec). Leaf size: 29

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

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