23.3.526 problem 532

Internal problem ID [6240]
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 : 532
Date solved : Tuesday, September 30, 2025 at 02:37:38 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (\operatorname {b1} \,x^{2}+\operatorname {b0} \right ) y+\left (\operatorname {a2} \,x^{2}+\operatorname {a1} x +\operatorname {a0} \right ) y^{\prime }+4 \left (1-x \right ) x \left (-a x +1\right ) y^{\prime \prime }&=0 \end{align*}

✗ Maple

ode:=(b1*x^2+b0)*y(x)+(a2*x^2+a1*x+a0)*diff(y(x),x)+4*(1-x)*x*(-a*x+1)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(b0 + b1*x^2)*y[x] + (a0 + a1*x + a2*x^2)*D[y[x],x] + 4*(1 - x)*x*(1 - a*x)*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") 
a2 = symbols("a2") 
b0 = symbols("b0") 
b1 = symbols("b1") 
y = Function("y") 
ode = Eq(x*(4 - 4*x)*(-a*x + 1)*Derivative(y(x), (x, 2)) + (b0 + b1*x**2)*y(x) + (a0 + a1*x + a2*x**2)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Expected Expr or iterable but got None