23.3.524 problem 530

Internal problem ID [6238]
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 : 530
Date solved : Tuesday, September 30, 2025 at 02:37:36 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 \left (b x +3 a \right ) y-2 x \left (b x +2 a \right ) y^{\prime }+x^{2} \left (b x +a \right ) y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

ode:=2*(b*x+3*a)*y(x)-2*x*(b*x+2*a)*diff(y(x),x)+x^2*(b*x+a)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 23

ode=2*(3*a + b*x)*y[x] - 2*x*(2*a + b*x)*D[y[x],x] + x^2*(a + b*x)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^2 (c_2 x+c_1)}{a+b x} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
y = Function("y") 
ode = Eq(x**2*(a + b*x)*Derivative(y(x), (x, 2)) - 2*x*(2*a + b*x)*Derivative(y(x), x) + (6*a + 2*b*x)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False