23.3.553 problem 560

Internal problem ID [6267]
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 : 560
Date solved : Friday, October 03, 2025 at 01:58:04 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.036 (sec). Leaf size: 413

ode:=(c2*x^2+b2*x+a2)*y(x)+a1*x*(-x^2+1)*diff(y(x),x)+(-x^2+1)^2*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 115.464 (sec). Leaf size: 1166395

ode=(a2 + b2*x + c2*x^2)*y[x] + a1*x*(1 - x^2)*D[y[x],x] + (1 - x^2)^2*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
a1 = symbols("a1") 
a2 = symbols("a2") 
b2 = symbols("b2") 
c2 = symbols("c2") 
y = Function("y") 
ode = Eq(a1*x*(1 - x**2)*Derivative(y(x), x) + (1 - x**2)**2*Derivative(y(x), (x, 2)) + (a2 + b2*x + c2*x**2)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False