73.23.5 problem 33.3 (e)

Internal problem ID [15651]
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 : 33.3 (e)
Date solved : Tuesday, January 28, 2025 at 08:03:39 AM
CAS classification : [_separable]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 12

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

\[ y = y \left (0\right ) \left (x^{2}+1\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 11

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

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