23.3.322 problem 324

Internal problem ID [6036]
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 : 324
Date solved : Friday, October 03, 2025 at 01:45:53 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 57

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

\[ y = {\mathrm e}^{-\frac {x}{2}} \sqrt {x}\, \left (\operatorname {BesselY}\left (\frac {\sqrt {-4 a +1}}{2}, \frac {\sqrt {4 b -1}\, x}{2}\right ) c_2 +\operatorname {BesselJ}\left (\frac {\sqrt {-4 a +1}}{2}, \frac {\sqrt {4 b -1}\, x}{2}\right ) c_1 \right ) \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 85

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

\begin{align*} y(x)&\to e^{-x/2} \sqrt {x} \left (c_1 \operatorname {BesselJ}\left (\frac {1}{2} \sqrt {1-4 a},-\frac {1}{2} i \sqrt {1-4 b} x\right )+c_2 \operatorname {BesselY}\left (\frac {1}{2} \sqrt {1-4 a},-\frac {1}{2} i \sqrt {1-4 b} x\right )\right ) \end{align*}

✗ Sympy

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

ValueError : Expected Expr or iterable but got None