78.15.16 problem 19 (a)

Internal problem ID [18293]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 22. Higher Order Linear Equations. Coupled Harmonic Oscillators. Problems at page 160
Problem number : 19 (a)
Date solved : Thursday, March 13, 2025 at 11:53:08 AM
CAS classification : [[_high_order, _quadrature]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

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

\[ y = \frac {1}{6} c_{1} x^{3}+\frac {1}{2} c_{2} x^{2}+c_3 x +c_4 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 22

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

\[ y(x)\to x (x (c_4 x+c_3)+c_2)+c_1 \]

✓ Sympy. Time used: 0.049 (sec). Leaf size: 17

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

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