73.23.15 problem 33.5 (c)

Internal problem ID [15590]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 33. Power series solutions I: Basic computational methods. Additional Exercises. page 641
Problem number : 33.5 (c)
Date solved : Monday, March 31, 2025 at 01:41:52 PM
CAS classification : [[_2nd_order, _missing_y]]

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

Using series method with expansion around

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 26

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

\[ y = y \left (0\right )+\left (x -\frac {1}{12} x^{3}+\frac {1}{80} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 25

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

\[ y(x)\to c_2 \left (\frac {x^5}{80}-\frac {x^3}{12}+x\right )+c_1 \]

✓ Sympy. Time used: 0.802 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = C_{2} x \left (1 - \frac {x^{2}}{12}\right ) + C_{1} + O\left (x^{6}\right ) \]