64.10.24 problem 24

Internal problem ID [13351]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients. Exercises page 135
Problem number : 24
Date solved : Wednesday, March 05, 2025 at 09:48:37 PM
CAS classification : [[_high_order, _quadrature]]

\begin{align*} y^{\left (5\right )}&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 27

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

\[ y = \frac {1}{24} c_{1} x^{4}+\frac {1}{6} c_{2} x^{3}+\frac {1}{2} c_{3} x^{2}+c_4 x +c_5 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 27

ode=D[y[x],{x,5}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x (x (x (c_5 x+c_4)+c_3)+c_2)+c_1 \]

✓ Sympy. Time used: 0.066 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 5)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + C_{4} x^{3} + C_{5} x^{4} \]