Internal problem ID [2398]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 11, Series Solutions to Linear Differential Equations. Exercises for 11.2. page
739
Problem number: Problem 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Gegenbauer]
Solve \begin {gather*} \boxed {\left (-4 x^{2}+1\right ) y^{\prime \prime }-20 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: 0.003 (sec). Leaf size: 34
Order:=6; dsolve((1-4*x^2)*diff(y(x),x$2)-20*x*diff(y(x),x)-16*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+8 x^{2}+\frac {128}{3} x^{4}\right ) y \relax (0)+\left (30 x^{5}+6 x^{3}+x \right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 36
AsymptoticDSolveValue[(1-4*x^2)*y''[x]-20*x*y'[x]-16*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (30 x^5+6 x^3+x\right )+c_1 \left (\frac {128 x^4}{3}+8 x^2+1\right ) \]