88.25.11 problem 9

Internal problem ID [24216]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 7. Series Methods. Exercises at page 212
Problem number : 9
Date solved : Thursday, October 02, 2025 at 10:00:53 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 47

Order:=6; 
ode:=25*x^2*diff(diff(y(x),x),x)+(4+2*x)*y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

\[ y = c_1 \,x^{{1}/{5}} \left (1-\frac {1}{5} x +\frac {1}{175} x^{2}-\frac {1}{15750} x^{3}+\frac {1}{2677500} x^{4}-\frac {1}{736312500} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_2 \,x^{{4}/{5}} \left (1-\frac {1}{20} x +\frac {1}{1300} x^{2}-\frac {1}{175500} x^{3}+\frac {1}{40365000} x^{4}-\frac {1}{14127750000} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 90

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

\[ y(x)\to c_2 \sqrt [5]{x} \left (-\frac {x^5}{736312500}+\frac {x^4}{2677500}-\frac {x^3}{15750}+\frac {x^2}{175}-\frac {x}{5}+1\right )+c_1 x^{4/5} \left (-\frac {x^5}{14127750000}+\frac {x^4}{40365000}-\frac {x^3}{175500}+\frac {x^2}{1300}-\frac {x}{20}+1\right ) \]

✓ Sympy. Time used: 0.322 (sec). Leaf size: 60

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(25*x**2*Derivative(y(x), (x, 2)) + (2*x + 4)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=6)
 

\[ y{\left (x \right )} = C_{2} x^{\frac {4}{5}} \left (\frac {x^{4}}{40365000} - \frac {x^{3}}{175500} + \frac {x^{2}}{1300} - \frac {x}{20} + 1\right ) + C_{1} \sqrt [5]{x} \left (\frac {x^{4}}{2677500} - \frac {x^{3}}{15750} + \frac {x^{2}}{175} - \frac {x}{5} + 1\right ) + O\left (x^{6}\right ) \]