28.2.8 problem 8

Internal problem ID [4451]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 8
Date solved : Tuesday, March 04, 2025 at 06:44:20 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime }+16 y&=0 \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 48

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-4*diff(diff(y(x),x),x)+16*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = -c_{1} {\mathrm e}^{\sqrt {3}\, x} \sin \left (x \right )+c_{2} {\mathrm e}^{-\sqrt {3}\, x} \sin \left (x \right )+c_3 \,{\mathrm e}^{\sqrt {3}\, x} \cos \left (x \right )+c_4 \,{\mathrm e}^{-\sqrt {3}\, x} \cos \left (x \right ) \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 55

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

\[ y(x)\to e^{-\sqrt {3} x} \left (\left (c_3 e^{2 \sqrt {3} x}+c_2\right ) \cos (x)+\left (c_1 e^{2 \sqrt {3} x}+c_4\right ) \sin (x)\right ) \]

✓ Sympy. Time used: 0.171 (sec). Leaf size: 39

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

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