23.3.561 problem 568

Internal problem ID [6275]
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 : 568
Date solved : Tuesday, September 30, 2025 at 02:42:03 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 33

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

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

✓ Mathematica. Time used: 2.027 (sec). Leaf size: 39

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

\begin{align*} y(x)&\to c_1 \cosh (\log (1-x)-\log (x))+i c_2 \sinh (\log (1-x)-\log (x)) \end{align*}

✗ Sympy

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

False