Internal problem ID [13595]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime }-2 y x=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
Order:=6; dsolve((1+x^2)*diff(y(x),x)-2*x*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = y \left (0\right ) \left (x^{2}+1\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 11
AsymptoticDSolveValue[(1+x^2)*y'[x]-2*x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (x^2+1\right ) \]