73.23.15 problem 33.5 (c)

Internal problem ID [15661]
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 : Tuesday, January 28, 2025 at 08:03:48 AM
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*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

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

AsymptoticDSolveValue[(4+x^2)*D[y[x],{x,2}]+2*x*D[y[x],x]==0,y[x],{x,0,"6"-1}]
 

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