23.3.508 problem 514

Internal problem ID [6222]
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 : 514
Date solved : Tuesday, September 30, 2025 at 02:36:40 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

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

\[ y = x \left (c_2 \ln \left (x \right )+c_2 x +c_1 \right ) \]

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 17

ode=(1 + 2*x)*y[x] - x*(1 + 2*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 x (c_2 (x+\log (x))+c_1) \end{align*}

✗ Sympy

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

False