23.5.86 problem 86

Internal problem ID [6695]
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 : 86
Date solved : Tuesday, September 30, 2025 at 03:50:54 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✗ Maple

ode:=2*x^3*y(x)+(-2*x^3+6)*diff(y(x),x)+x*(-x^2+6)*diff(diff(y(x),x),x)+x^2*diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : The given ODE -x*(2*x**2*y(x) - x**2*Derivative(y(x), (x, 2)) + x*Derivative(y