84.30.6 problem 18.16

Internal problem ID [22295]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 18. Linear differential equations with variable coefficients. Supplementary problems
Problem number : 18.16
Date solved : Thursday, October 02, 2025 at 08:37:13 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{3} y^{\prime \prime }+y x&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 34

Order:=6; 
ode:=x^3*diff(diff(y(x),x),x)+x*y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = \sqrt {x}\, \left (c_1 \,x^{-\frac {i \sqrt {3}}{2}}+c_2 \,x^{\frac {i \sqrt {3}}{2}}\right )+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 26

ode=x^3*D[y[x],{x,2}]+x*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_1 x^{-(-1)^{2/3}}+c_2 x^{\sqrt [3]{-1}} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**3*Derivative(y(x), (x, 2)) + x*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=6)
 

ValueError : Expected Expr or iterable but got None