12.18.30 problem section 9.2, problem 43(c)

Internal problem ID [2144]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient. Page 483
Problem number : section 9.2, problem 43(c)
Date solved : Tuesday, March 04, 2025 at 01:50:47 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+64 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 41

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+64*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 44

ode=D[y[x],{x,4}]+64*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-2 x} \left (\left (c_4 e^{4 x}+c_1\right ) \cos (2 x)+\left (c_3 e^{4 x}+c_2\right ) \sin (2 x)\right ) \]

✓ Sympy. Time used: 0.137 (sec). Leaf size: 39

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(64*y(x) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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