69.15.19 problem 450

Internal problem ID [18257]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.2 Homogeneous differential equations with constant coefficients. Exercises page 121
Problem number : 450
Date solved : Thursday, October 02, 2025 at 03:09:51 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]
 

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

✓ Sympy. Time used: 0.028 (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)
 

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