23.3.575 problem 583

Internal problem ID [6289]
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 : 583
Date solved : Tuesday, September 30, 2025 at 02:44:59 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (-2 x^{3}+1\right ) y-x \left (-2 x^{3}+1\right ) y^{\prime }+x^{5} y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 16

ode:=(-2*x^3+1)*y(x)-x*(-2*x^3+1)*diff(y(x),x)+x^5*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x \left ({\mathrm e}^{-\frac {1}{3 x^{3}}} c_2 +c_1 \right ) \]

✓ Mathematica. Time used: 0.048 (sec). Leaf size: 22

ode=(1 - 2*x^3)*y[x] - x*(1 - 2*x^3)*D[y[x],x] + x^5*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x \left (c_2 e^{-\frac {1}{3 x^3}}+c_1\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**5*Derivative(y(x), (x, 2)) - x*(1 - 2*x**3)*Derivative(y(x), x) + (1 - 2*x**3)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**5*Derivative(y(x), (x, 2)) + 2*x**3*y