23.5.186 problem 186

Internal problem ID [6795]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 186
Date solved : Tuesday, September 30, 2025 at 03:51:45 PM
CAS classification : [[_high_order, _quadrature]]

\begin{align*} y^{\left (6\right )}&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 33

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

\[ y = \frac {1}{120} c_1 \,x^{5}+\frac {1}{24} c_2 \,x^{4}+\frac {1}{6} c_3 \,x^{3}+\frac {1}{2} c_4 \,x^{2}+c_5 x +c_6 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 32

ode=D[y[x],{x,6}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x (x (x (x (c_6 x+c_5)+c_4)+c_3)+c_2)+c_1 \end{align*}

✓ Sympy. Time used: 0.044 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 6)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + C_{4} x^{3} + C_{5} x^{4} + C_{6} x^{5} \]