47.4.8 problem 56

Internal problem ID [7485]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 2. Linear homogeneous equations. Section 2.2 problems. page 95
Problem number : 56
Date solved : Wednesday, March 05, 2025 at 04:39:53 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-2 x y^{\prime \prime }+4 x^{2} y^{\prime }+8 x^{3} y&=0 \end{align*}

✗ Maple

ode:=diff(diff(diff(y(x),x),x),x)-2*x*diff(diff(y(x),x),x)+4*x^2*diff(y(x),x)+8*x^3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],{x,3}]-2*x*D[y[x],{x,2}]+4*x^2*D[y[x],x]+8*x^3*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(8*x**3*y(x) + 4*x**2*Derivative(y(x), x) - 2*x*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE 2*x*y(x) + Derivative(y(x), x) - Derivative(y(x), (x, 2))/(2*x) + Derivative(y(x), (x, 3))/(4*x**2) cannot be solved by the factorable group method