28.2.6 problem 6

Internal problem ID [4449]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 6
Date solved : Tuesday, March 04, 2025 at 06:44:19 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 33

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

\[ y \left (x \right ) = c_{1} \sin \left (x \right ) {\mathrm e}^{-x}+c_{2} {\mathrm e}^{-x} \cos \left (x \right )+c_3 \sin \left (x \right ) {\mathrm e}^{x}+c_4 \cos \left (x \right ) {\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 40

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

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

✓ Sympy. Time used: 0.103 (sec). Leaf size: 29

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

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