23.3.557 problem 564

Internal problem ID [6271]
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 : 564
Date solved : Tuesday, September 30, 2025 at 02:39:24 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+x \left (\operatorname {b0} \,x^{2}+\operatorname {a0} \right ) y^{\prime }+\left (a^{2}+x^{2}\right )^{2} \left (b^{2}+x^{2}\right ) y^{\prime \prime }&=0 \end{align*}

✗ Maple

ode:=(b1*x^2+a1)*y(x)+x*(b0*x^2+a0)*diff(y(x),x)+(a^2+x^2)^2*(b^2+x^2)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(a1 + b1*x^2)*y[x] + x*(a0 + b0*x^2)*D[y[x],x] + (a^2 + x^2)^2*(b^2 + x^2)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
a0 = symbols("a0") 
a1 = symbols("a1") 
b = symbols("b") 
b0 = symbols("b0") 
b1 = symbols("b1") 
y = Function("y") 
ode = Eq(x*(a0 + b0*x**2)*Derivative(y(x), x) + (a**2 + x**2)**2*(b**2 + x**2)*Derivative(y(x), (x, 2)) + (a1 + b1*x**2)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out