23.3.562 problem 569

Internal problem ID [6276]
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 : 569
Date solved : Friday, October 03, 2025 at 01:58:10 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.037 (sec). Leaf size: 371

ode:=(c2*x^2+b2*x+a2)*y(x)+(1-x)*x*(b2*x+a1)*diff(y(x),x)+(1-x)^2*x^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: 133.073 (sec). Leaf size: 2310040

ode=(a2 + b2*x + c2*x^2)*y[x] + (1 - x)*x*(a1 + b2*x)*D[y[x],x] + (1 - x)^2*x^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(x**2*(1 - x)**2*Derivative(y(x), (x, 2)) + x*(1 - x)*(a1 + b2*x)*Derivative(y(x), x) + (a2 + b2*x + c2*x**2)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Expected Expr or iterable but got None