85.45.5 problem 2 (f)

Internal problem ID [22788]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 180
Problem number : 2 (f)
Date solved : Thursday, October 02, 2025 at 09:14:39 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} s^{\prime \prime \prime \prime }+2 s^{\prime \prime }-8 s&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 34

ode:=diff(diff(diff(diff(s(x),x),x),x),x)+2*diff(diff(s(x),x),x)-8*s(x) = 0; 
dsolve(ode,s(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 45

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

\begin{align*} s(x)&\to c_3 e^{\sqrt {2} x}+c_4 e^{-\sqrt {2} x}+c_1 \cos (2 x)+c_2 \sin (2 x) \end{align*}

✓ Sympy. Time used: 0.082 (sec). Leaf size: 36

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

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