64.10.18 problem 18

Internal problem ID [13345]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 18
Date solved : Wednesday, March 05, 2025 at 09:48:33 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y&=0 \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 25

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+8*diff(diff(y(x),x),x)+16*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 30

ode=D[y[x],{x,4}]+8*D[y[x],{x,2}]+16*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to (c_2 x+c_1) \cos (2 x)+(c_4 x+c_3) \sin (2 x) \]

✓ Sympy. Time used: 0.089 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*y(x) + 8*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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