23.3.394 problem 398

Internal problem ID [6108]
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 : 398
Date solved : Tuesday, September 30, 2025 at 02:21:39 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 22

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

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 26

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

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

✗ Sympy

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

False