76.23.8 problem 9

Internal problem ID [17728]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 6. Systems of First Order Linear Equations. Section 6.1 (Definitions and examples). Problems at page 388
Problem number : 9
Date solved : Monday, March 31, 2025 at 04:26:06 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}-2\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+3 y&=0 \end{align*}

✗ Maple

ode:=(x^2-2)*diff(diff(diff(diff(diff(diff(y(x),x),x),x),x),x),x)+x^2*diff(diff(y(x),x),x)+3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(x^2-2)*D[y[x],{x,6}]+x^2*D[y[x],{x,2}]+3*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + (x**2 - 2)*Derivative(y(x), (x, 6)) + 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve x**2*Derivative(y(x), (x, 2)) + (x**2 - 2)*Derivative(y(x), (x, 6)) + 3*y(x)