23.3.580 problem 588

Internal problem ID [6294]
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 : 588
Date solved : Friday, October 03, 2025 at 02:00:21 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\left (a -x \right ) \left (b -x \right ) \left (c -x \right ) \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (a -x \right )^{2} \left (b -x \right )^{2} \left (c -x \right )^{2} y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 8.949 (sec). Leaf size: 9064

ode:=(c2*x^2+b2*x+a2)*y(x)+(a-x)*(b-x)*(c-x)*(c1*x^2+b1*x+a1)*diff(y(x),x)+(a-x)^2*(b-x)^2*(c-x)^2*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {Expression too large to display} \]

✓ Mathematica. Time used: 138.17 (sec). Leaf size: 18649

ode=(a2 + b2*x + c2*x^2)*y[x] + (a - x)*(b - x)*(c - x)*(a1 + b1*x + c1*x^2)*D[y[x],x] + (a - x)^2*(b - x)^2*(c - 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") 
a = symbols("a") 
a1 = symbols("a1") 
a2 = symbols("a2") 
b = symbols("b") 
b1 = symbols("b1") 
b2 = symbols("b2") 
c = symbols("c") 
c1 = symbols("c1") 
c2 = symbols("c2") 
y = Function("y") 
ode = Eq((a - x)**2*(b - x)**2*(c - x)**2*Derivative(y(x), (x, 2)) + (a - x)*(b - x)*(c - x)*(a1 + b1*x + c1*x**2)*Derivative(y(x), x) + (a2 + b2*x + c2*x**2)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False