23.3.455 problem 460

Internal problem ID [6169]
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 : 460
Date solved : Tuesday, September 30, 2025 at 02:24:01 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

ode:=(x^4+2*x^2+1)*y(x)+4*x^3*diff(y(x),x)+4*x^2*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 28

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

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

✗ Sympy

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

False