23.3.452 problem 457

Internal problem ID [6166]
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 : 457
Date solved : Tuesday, September 30, 2025 at 02:23:59 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (3+x \right ) y-2 x \left (2+x \right ) y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 16

ode:=(x+3)*y(x)-2*x*(x+2)*diff(y(x),x)+4*x^2*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 25

ode=(3 + x)*y[x] - 2*x*(2 + x)*D[y[x],x] + 4*x^2*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \sqrt {x} \left (2 c_2 e^{x/2}+c_1\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**2*Derivative(y(x), (x, 2)) - 2*x*(x + 2)*Derivative(y(x), x) + (x + 3)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False