23.3.510 problem 516

Internal problem ID [6224]
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 : 516
Date solved : Tuesday, September 30, 2025 at 02:36:41 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (6-9 x \right ) y-\left (4-5 x \right ) x y^{\prime }+\left (1-x \right ) x^{2} y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

ode:=(6-9*x)*y(x)-(4-5*x)*x*diff(y(x),x)+(1-x)*x^2*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 24

ode=(6 - 9*x)*y[x] - (4 - 5*x)*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 x^2 (c_1 x-c_2 (x \log (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*(4 - 5*x)*Derivative(y(x), x) + (6 - 9*x)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False