23.3.256 problem 258

Internal problem ID [5970]
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 : 258
Date solved : Friday, October 03, 2025 at 01:45:43 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (c \,x^{2}+b x +a \right ) y+x^{2} y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.041 (sec). Leaf size: 57

ode:=(c*x^2+b*x+a)*y(x)+x^2*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \operatorname {WhittakerM}\left (-\frac {i b}{2 \sqrt {c}}, \frac {\sqrt {1-4 a}}{2}, 2 i \sqrt {c}\, x \right )+c_2 \operatorname {WhittakerW}\left (-\frac {i b}{2 \sqrt {c}}, \frac {\sqrt {1-4 a}}{2}, 2 i \sqrt {c}\, x \right ) \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 88

ode=(a + b*x + c*x^2)*y[x] + x^2*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 M_{-\frac {i b}{2 \sqrt {c}},-\frac {1}{2} i \sqrt {4 a-1}}\left (2 i \sqrt {c} x\right )+c_2 W_{-\frac {i b}{2 \sqrt {c}},-\frac {1}{2} i \sqrt {4 a-1}}\left (2 i \sqrt {c} x\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + (a + b*x + c*x**2)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Expected Expr or iterable but got None