23.3.411 problem 416

Internal problem ID [6125]
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 : 416
Date solved : Tuesday, September 30, 2025 at 02:21:58 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 32

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

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 37

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

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

✗ Sympy

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

False