28.2.12 problem 12

Internal problem ID [4455]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 12
Date solved : Sunday, March 30, 2025 at 03:23:01 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (6\right )}-64 y&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 53

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

\[ y = {\mathrm e}^{-2 x} \left (\left ({\mathrm e}^{3 x} c_6 +c_4 \,{\mathrm e}^{x}\right ) \cos \left (\sqrt {3}\, x \right )+\left ({\mathrm e}^{3 x} c_5 +c_3 \,{\mathrm e}^{x}\right ) \sin \left (\sqrt {3}\, x \right )+c_2 \,{\mathrm e}^{4 x}+c_1 \right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 68

ode=D[y[x],{x,6}]-64*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-2 x} \left (c_1 e^{4 x}+e^x \left (c_2 e^{2 x}+c_3\right ) \cos \left (\sqrt {3} x\right )+e^x \left (c_6 e^{2 x}+c_5\right ) \sin \left (\sqrt {3} x\right )+c_4\right ) \]

✓ Sympy. Time used: 0.223 (sec). Leaf size: 63

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-64*y(x) + Derivative(y(x), (x, 6)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{5} e^{- 2 x} + C_{6} e^{2 x} + \left (C_{1} \sin {\left (\sqrt {3} x \right )} + C_{2} \cos {\left (\sqrt {3} x \right )}\right ) e^{- x} + \left (C_{3} \sin {\left (\sqrt {3} x \right )} + C_{4} \cos {\left (\sqrt {3} x \right )}\right ) e^{x} \]