Internal problem ID [439]
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 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x +2 y x=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 39
Order:=6; dsolve((x^2-1)*diff(y(x),x$2)+2*x*diff(y(x),x)+2*x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+\frac {1}{3} x^{3}+\frac {1}{5} x^{5}\right ) y \relax (0)+\left (x +\frac {1}{3} x^{3}+\frac {1}{6} x^{4}+\frac {1}{5} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 49
AsymptoticDSolveValue[(x^2+1)*y''[x]+2*x*y'[x]+2*x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^5}{5}-\frac {x^3}{3}+1\right )+c_2 \left (\frac {x^5}{5}-\frac {x^4}{6}-\frac {x^3}{3}+x\right ) \]