Internal problem ID [4715]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 27. Power series solutions of linear DE with variable coefficients. Supplementary
Problems. page 274
Problem number: Problem 27.41.
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 }+x y^{\prime }-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: 24
Order:=6; dsolve((x^2-1)*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {1}{2} x^{2}-\frac {1}{8} x^{4}\right ) y \relax (0)+D\relax (y )\relax (0) x +O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 27
AsymptoticDSolveValue[(x^2-1)*y''[x]+x*y'[x]-y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {x^4}{8}-\frac {x^2}{2}+1\right )+c_2 x \]