35.9.17 problem 9, using series method

Internal problem ID [6252]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 12, Series Solutions of Differential Equations. Section 1. Miscellaneous problems. page 564
Problem number : 9, using series method
Date solved : Monday, January 27, 2025 at 01:50:08 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 18

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

\[ y = y \left (0\right )+y^{\prime }\left (0\right ) x -y \left (0\right ) x^{2} \]

✓ Solution by Mathematica

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

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

\[ y(x)\to c_1 \left (1-x^2\right )+c_2 x \]