23.3.278 problem 280

Internal problem ID [5992]
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 : 280
Date solved : Friday, October 03, 2025 at 01:45:47 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} -\left (c^{2} x^{4}+b^{2} x^{2}+a^{2}\right ) y+x y^{\prime }+x^{2} y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 47

ode:=-(c^2*x^4+b^2*x^2+a^2)*y(x)+x*diff(y(x),x)+x^2*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.149 (sec). Leaf size: 96

ode=-((a^2 + b^2*x^2 + c^2*x^4)*y[x]) + x*D[y[x],x] + x^2*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2^{\frac {a+1}{2}} \left (x^2\right )^{\frac {a+1}{2}} e^{-\frac {c x^2}{2}} \left (c_1 \operatorname {HypergeometricU}\left (\frac {b^2+2 (a+1) c}{4 c},a+1,c x^2\right )+c_2 L_{-\frac {b^2+2 (a+1) c}{4 c}}^a\left (c x^2\right )\right )}{x} \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)) + x*Derivative(y(x), x) + (-a**2 - b**2*x**2 - c**2*x**4)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Expected Expr or iterable but got None