60.3.387 problem 1404

Internal problem ID [11383]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1404
Date solved : Sunday, March 30, 2025 at 08:19:15 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

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

\[ y = {\mathrm e}^{\frac {1}{4 x^{2}}} \left (c_1 +\frac {c_2}{x}\right ) \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 25

ode=D[y[x],{x,2}] == -1/4*((1 - 2*x^2)*y[x])/x^6 - ((1 + 2*x^2)*D[y[x],x])/x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {e^{\frac {1}{4 x^2}} (c_2 x+c_1)}{x} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 2)) + (2*x**2 + 1)*Derivative(y(x), x)/x**3 + (1 - 2*x**2)*y(x)/(4*x**6),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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