12.18.31 problem section 9.2, problem 43(d)

Internal problem ID [2145]
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(d)
Date solved : Tuesday, March 04, 2025 at 01:50:48 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 59

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

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 78

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

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

✓ Sympy. Time used: 0.223 (sec). Leaf size: 70

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

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