23.3.518 problem 524

Internal problem ID [6232]
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 : 524
Date solved : Friday, October 03, 2025 at 01:57:47 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (\operatorname {c1} x +\operatorname {c0} \right ) y+\left (\operatorname {b2} \,x^{2}+\operatorname {b1} x +\operatorname {b0} \right ) y^{\prime }+\left (\operatorname {a1} -x \right ) \left (\operatorname {a2} -x \right ) \left (\operatorname {a3} -x \right ) y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.320 (sec). Leaf size: 1121

ode:=(c1*x+c0)*y(x)+(b2*x^2+b1*x+b0)*diff(y(x),x)+(a1-x)*(a2-x)*(a3-x)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 7.141 (sec). Leaf size: 1131

ode=(c0 + c1*x)*y[x] + (b0 + b1*x + b2*x^2)*D[y[x],x] + (a1 - x)*(a2 - x)*(a3 - x)*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") 
a3 = symbols("a3") 
b0 = symbols("b0") 
b1 = symbols("b1") 
b2 = symbols("b2") 
c0 = symbols("c0") 
c1 = symbols("c1") 
y = Function("y") 
ode = Eq((a1 - x)*(a2 - x)*(a3 - x)*Derivative(y(x), (x, 2)) + (c0 + c1*x)*y(x) + (b0 + b1*x + b2*x**2)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False