88.16.2 problem 2

Internal problem ID [24107]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 4. Linear equations. Exercises at page 116
Problem number : 2
Date solved : Thursday, October 02, 2025 at 09:59:18 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (8\right )}-y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 84

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

\[ y = \left (-c_5 \,{\mathrm e}^{-\frac {\sqrt {2}\, x}{2}}-c_6 \,{\mathrm e}^{\frac {\sqrt {2}\, x}{2}}\right ) \sin \left (\frac {\sqrt {2}\, x}{2}\right )+c_7 \,{\mathrm e}^{-\frac {\sqrt {2}\, x}{2}} \cos \left (\frac {\sqrt {2}\, x}{2}\right )+c_8 \,{\mathrm e}^{\frac {\sqrt {2}\, x}{2}} \cos \left (\frac {\sqrt {2}\, x}{2}\right )+c_4 \cos \left (x \right )+c_2 \,{\mathrm e}^{x}+c_3 \sin \left (x \right )+c_1 \,{\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 105

ode=D[y[x],{x,8}]-y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^x+c_5 e^{-x}+c_3 \cos (x)+e^{-\frac {x}{\sqrt {2}}} \left (c_2 e^{\sqrt {2} x}+c_4\right ) \cos \left (\frac {x}{\sqrt {2}}\right )+c_7 \sin (x)+c_6 e^{-\frac {x}{\sqrt {2}}} \sin \left (\frac {x}{\sqrt {2}}\right )+c_8 e^{\frac {x}{\sqrt {2}}} \sin \left (\frac {x}{\sqrt {2}}\right ) \end{align*}

✓ Sympy. Time used: 0.168 (sec). Leaf size: 90

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

\[ y{\left (x \right )} = C_{5} e^{- x} + C_{6} e^{x} + C_{7} \sin {\left (x \right )} + C_{8} \cos {\left (x \right )} + \left (C_{1} \sin {\left (\frac {\sqrt {2} x}{2} \right )} + C_{2} \cos {\left (\frac {\sqrt {2} x}{2} \right )}\right ) e^{- \frac {\sqrt {2} x}{2}} + \left (C_{3} \sin {\left (\frac {\sqrt {2} x}{2} \right )} + C_{4} \cos {\left (\frac {\sqrt {2} x}{2} \right )}\right ) e^{\frac {\sqrt {2} x}{2}} \]