23.3.582 problem 590

Internal problem ID [6296]
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 : 590
Date solved : Tuesday, September 30, 2025 at 02:45:11 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (8 x^{4}+10 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: 0.003 (sec). Leaf size: 17

ode:=(8*x^4+10*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);
 

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 23

ode=(1 + 10*x^2 + 8*x^4)*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 e^{-\frac {1}{4 x^2}} x (c_2 x+c_1) \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) + (8*x**4 + 10*x**2 + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (4*x**6*Derivative(y(x), (x, 2)) + 8*x**4*