23.3.576 problem 584

Internal problem ID [6290]
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 : 584
Date solved : Tuesday, September 30, 2025 at 02:45:00 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{3} \left (\operatorname {c1} \,x^{4}+\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+\left (\operatorname {b0} \,x^{4}+\operatorname {a0} \right ) y^{\prime }+x \left (a^{2}-x^{2}\right ) \left (b^{2}-x^{2}\right ) y^{\prime \prime }&=0 \end{align*}

✗ Maple

ode:=x^3*(c1*x^4+b1*x^2+a1)*y(x)+(b0*x^4+a0)*diff(y(x),x)+x*(a^2-x^2)*(b^2-x^2)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=x^3*(a1 + b1*x^2 + c1*x^4)*y[x] + (a0 + b0*x^4)*D[y[x],x] + x*(a^2 - x^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") 
c1 = symbols("c1") 
y = Function("y") 
ode = Eq(x**3*(a1 + b1*x**2 + c1*x**4)*y(x) + x*(a**2 - x**2)*(b**2 - x**2)*Derivative(y(x), (x, 2)) + (a0 + b0*x**4)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Expected Expr or iterable but got None