23.3.199 problem 201

Internal problem ID [5913]
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 : 201
Date solved : Tuesday, September 30, 2025 at 02:06:07 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✗ Maple

ode:=(c1*x^2+b1*x+a1)*y(x)+a*diff(y(x),x)+x*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

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

ValueError : Expected Expr or iterable but got None