23.3.511 problem 517

Internal problem ID [6225]
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 : 517
Date solved : Tuesday, September 30, 2025 at 02:36:42 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} 2 \left (1+3 x \right ) y+2 x \left (2+3 x \right ) y^{\prime }+x^{2} \left (1+x \right ) y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=2*(3*x+1)*y(x)+2*x*(2+3*x)*diff(y(x),x)+x^2*(1+x)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 x +c_2}{x^{2} \left (1+x \right )} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 22

ode=2*(1 + 3*x)*y[x] + 2*x*(2 + 3*x)*D[y[x],x] + x^2*(1 + x)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_2 x+c_1}{x^3+x^2} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*(x + 1)*Derivative(y(x), (x, 2)) + 2*x*(3*x + 2)*Derivative(y(x), x) + (6*x + 2)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False