23.3.439 problem 444

Internal problem ID [6153]
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 : 444
Date solved : Tuesday, September 30, 2025 at 02:23:48 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 37

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

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

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 39

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

\begin{align*} y(x)&\to c_1 (2 x-1)+\frac {1}{4} c_2 (2 (x-1) x+(1-2 x) \log (1-2 x)) \end{align*}

✗ Sympy

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

False