73.25.18 problem 35.4 (d)

Internal problem ID [15655]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 35. Modified Power series solutions and basic method of Frobenius. Additional Exercises. page 715
Problem number : 35.4 (d)
Date solved : Monday, March 31, 2025 at 01:44:09 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (-9 x^{4}+x^{2}\right ) y^{\prime \prime }-6 x y^{\prime }+10 y&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.024 (sec). Leaf size: 35

Order:=6; 
ode:=(-9*x^4+x^2)*diff(diff(y(x),x),x)-6*x*diff(y(x),x)+10*y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = c_1 \,x^{5} \left (1+18 x^{2}+243 x^{4}+\operatorname {O}\left (x^{6}\right )\right )+c_2 \,x^{2} \left (12-108 x^{2}-2916 x^{4}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 38

ode=(x^2-9*x^4)*D[y[x],{x,2}]-6*x*D[y[x],x]+10*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_2 \left (243 x^9+18 x^7+x^5\right )+c_1 \left (-243 x^6-9 x^4+x^2\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*x*Derivative(y(x), x) + (-9*x**4 + x**2)*Derivative(y(x), (x, 2)) + 10*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