23.3.507 problem 513

Internal problem ID [6221]
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 : 513
Date solved : Tuesday, September 30, 2025 at 02:36:39 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

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

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

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 21

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

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

✗ Sympy

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

False