23.3.559 problem 566

Internal problem ID [6273]
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 : 566
Date solved : Tuesday, September 30, 2025 at 02:42:02 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 28

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

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

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 33

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

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(1 - x)*(x + 1)**2*Derivative(y(x), (x, 2)) + x*(6 - 2*x)*(x + 1)*Derivative(y(x), x) + (2*x - 2)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False