73.23.13 problem 33.5 (a)

Internal problem ID [15659]
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 (a)
Date solved : Tuesday, January 28, 2025 at 08:03:46 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }-2 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 32

Order:=6; 
dsolve((1+x^2)*diff(y(x),x$2)-2*y(x)=0,y(x),type='series',x=0);
 

\[ y = y \left (0\right ) \left (x^{2}+1\right )+\left (x +\frac {1}{3} x^{3}-\frac {1}{15} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 31

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

\[ y(x)\to c_1 \left (x^2+1\right )+c_2 \left (-\frac {x^5}{15}+\frac {x^3}{3}+x\right ) \]