56.4.54 problem 51

Internal problem ID [8943]
Book : Own collection of miscellaneous problems
Section : section 4.0
Problem number : 51
Date solved : Sunday, March 30, 2025 at 01:56:01 PM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-9 x y^{\prime }+25 y&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.032 (sec). Leaf size: 19

Order:=6; 
ode:=x^2*diff(diff(y(x),x),x)-9*x*diff(y(x),x)+25*y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = x^{5} \left (c_1 +c_2 \ln \left (x \right )\right )+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 18

ode=x^2*D[y[x],{x,2}]-9*x*D[y[x],x]+25*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,5}]
 

\[ y(x)\to c_1 x^5+c_2 x^5 \log (x) \]

✓ Sympy. Time used: 0.335 (sec). Leaf size: 3

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 9*x*Derivative(y(x), x) + 25*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=6)
 

\[ y{\left (x \right )} = O\left (1\right ) \]