Internal problem ID [423]
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 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {\left (-x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +16 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 34
Order:=6; dsolve((2-x^2)*diff(y(x),x$2)-x*diff(y(x),x)+16*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (2 x^{4}-4 x^{2}+1\right ) y \relax (0)+\left (x -\frac {5}{4} x^{3}+\frac {7}{32} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 38
AsymptoticDSolveValue[(2-x^2)*y''[x]-x*y'[x]+16*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {7 x^5}{32}-\frac {5 x^3}{4}+x\right )+c_1 \left (2 x^4-4 x^2+1\right ) \]