23.3.400 problem 404

Internal problem ID [6114]
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 : 404
Date solved : Tuesday, September 30, 2025 at 02:21:45 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

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

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

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 24

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

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

✗ Sympy

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

False