23.3.540 problem 546

Internal problem ID [6254]
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 : 546
Date solved : Tuesday, September 30, 2025 at 02:39:00 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 42

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

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

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 51

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

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

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (-b*y(x) - x**4*Derivative(y(x), (x, 2)))/