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]]
Solve \begin {gather*} \boxed {\left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (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);
\[ y \relax (x ) = \left (x^{4}+x^{2}+1\right ) y \relax (0)+\left (x^{5}+x^{3}+x \right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 62
AsymptoticDSolveValue[(x^2-1)*y''[x]+4*y'[x]+2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {28 x^5}{15}+\frac {5 x^4}{3}+\frac {4 x^3}{3}+x^2+1\right )+c_2 \left (\frac {62 x^5}{15}+\frac {11 x^4}{3}+3 x^3+2 x^2+x\right ) \]