50.13.7 problem 7

Internal problem ID [8022]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Section 2.7. HIGHER ORDER LINEAR EQUATIONS, COUPLED HARMONIC OSCILLATORS Page 98
Problem number : 7
Date solved : Wednesday, March 05, 2025 at 05:23:26 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

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

\[ y = c_{1} {\mathrm e}^{-x}+{\mathrm e}^{x} c_{2} +c_3 \sin \left (x \right )+c_4 \cos \left (x \right ) \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 30

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

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

✓ Sympy. Time used: 0.073 (sec). Leaf size: 22

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

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