82.52.1 problem Ex. 1

Internal problem ID [18930]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IX. Equations of the second order. problems at page 116
Problem number : Ex. 1
Date solved : Thursday, March 13, 2025 at 01:12:26 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+\frac {y^{\prime }}{x^{{1}/{3}}}+\left (\frac {1}{4 x^{{2}/{3}}}-\frac {1}{6 x^{{1}/{3}}}-\frac {6}{x^{2}}\right ) y&=0 \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x)+1/x^(1/3)*diff(y(x),x)+(1/4/x^(2/3)-1/6/x^(1/3)-6/x^2)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],{x,2}]+1/x^(1/3)*D[y[x],x]+( 1/(4*x^(2/3)) - 1/( 6*x^(1/3)) - 6/x^2)*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((-6/x**2 - 1/(6*x**(1/3)) + 1/(4*x**(2/3)))*y(x) + Derivative(y(x), (x, 2)) + Derivative(y(x), x)/x**(1/3),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE x**(1/3)*Derivative(y(x), (x, 2)) - y(x)/6 + Derivative(y(x), x) + y(x)/(4*x**(1/3)) - 6*y(x)/x**(5/3) cannot be solved by the factorable group method