46.2.6 problem 6

Internal problem ID [9543]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. 6.3 SOLUTIONS ABOUT SINGULAR POINTS. EXERCISES 6.3. Page 255
Problem number : 6
Date solved : Tuesday, September 30, 2025 at 06:20:28 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}-25\right ) y&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.031 (sec). Leaf size: 573

Order:=8; 
ode:=x^2*(x-5)^2*diff(diff(y(x),x),x)+4*x*diff(y(x),x)+(x^2-25)*y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 22488

ode=x^2*(x-5)^2*D[y[x],{x,2}]+4*x*D[y[x],x]+(x^2-25)*y[x]==0; 
ic={}; 
AsymptoticDSolveValue[{ode,ic},y[x],{x,0,7}]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*(x - 5)**2*Derivative(y(x), (x, 2)) + 4*x*Derivative(y(x), x) + (x**2 - 25)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=8)
 

NotImplementedError : Not sure of sign of 379/50 - x0