23.3.516 problem 522

Internal problem ID [6230]
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 : 522
Date solved : Tuesday, September 30, 2025 at 02:36:48 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 32

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

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

✗ Sympy

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

False