59.1.389 problem 400

Internal problem ID [9561]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 400
Date solved : Sunday, March 30, 2025 at 02:37:34 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 19

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

\[ y = x \left (c_1 +c_2 \,\operatorname {erf}\left (\frac {i \sqrt {2}}{2 x}\right )\right ) \]

✓ Mathematica. Time used: 0.082 (sec). Leaf size: 34

ode=x^3*D[y[x],{x,2}]+ D[y[x],x]-1/x*y[x] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 x-\sqrt {\frac {\pi }{2}} c_2 x \text {erfi}\left (\frac {1}{\sqrt {2} x}\right ) \]

✗ Sympy

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

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