23.3.581 problem 589

Internal problem ID [6295]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 589
Date solved : Tuesday, September 30, 2025 at 02:45:11 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=(-2*x^2+1)*y(x)+4*x^3*(2*x^2+1)*diff(y(x),x)+4*x^6*diff(diff(y(x),x),x) = 0; 
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: 0.022 (sec). Leaf size: 25

ode=(1 - 2*x^2)*y[x] + 4*x^3*(1 + 2*x^2)*D[y[x],x] + 4*x^6*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {e^{\frac {1}{4 x^2}} (c_2 x+c_1)}{x} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**6*Derivative(y(x), (x, 2)) + 4*x**3*(2*x**2 + 1)*Derivative(y(x), x) + (1 - 2*x**2)*y(x),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