Internal problem ID [416]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Chapter 11 Power series methods. Section 11.2 Power series solutions. Page 624
Problem number: problem 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {\left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
Order:=6; dsolve((x^2-1)*diff(y(x),x$2)+4*x*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (x^{4}+x^{2}+1\right ) y \left (0\right )+\left (x^{5}+x^{3}+x \right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 26
AsymptoticDSolveValue[(x^2-1)*y''[x]+4*x*y'[x]+2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (x^5+x^3+x\right )+c_1 \left (x^4+x^2+1\right ) \]