73.25.2 problem 35.2 (b)

Internal problem ID [15639]
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 : 35.2 (b)
Date solved : Monday, March 31, 2025 at 01:43:41 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y&=0 \end{align*}

Using series method with expansion around

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

✓ Maple. Time used: 0.030 (sec). Leaf size: 22

Order:=6; 
ode:=2*x^2*diff(diff(y(x),x),x)+5*x*diff(y(x),x)+y(x) = 0; 
dsolve(ode,y(x),type='series',x=0);
 

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

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 18

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

\[ y(x)\to \frac {c_1}{\sqrt {x}}+\frac {c_2}{x} \]

✓ Sympy. Time used: 0.759 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*Derivative(y(x), (x, 2)) + 5*x*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics,hint="2nd_power_series_regular",x0=0,n=6)
 

\[ y{\left (x \right )} = \frac {C_{2}}{\sqrt {x}} + \frac {C_{1}}{x} + O\left (x^{6}\right ) \]