23.3.453 problem 458

Internal problem ID [6167]
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 : 458
Date solved : Tuesday, September 30, 2025 at 02:24:00 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 21

ode=-((1 + 4*x - 4*x^2)*y[x]) + 4*(1 - 2*x)*x*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 \frac {e^x (c_2 x+c_1)}{\sqrt {x}} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**2*Derivative(y(x), (x, 2)) + x*(4 - 8*x)*Derivative(y(x), x) + (4*x**2 - 4*x - 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False