Internal problem ID [1208]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.2 SERIES SOLUTIONS NEAR AN
ORDINARY POINT I. Exercises 7.2. Page 329
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Gegenbauer]
Solve \begin {gather*} \boxed {\left (-x^{2}+1\right ) y^{\prime \prime }-8 y^{\prime } x -12 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 34
Order:=6; dsolve((1-x^2)*diff(y(x),x$2)-8*x*diff(y(x),x)-12*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (15 x^{4}+6 x^{2}+1\right ) y \relax (0)+\left (x +\frac {10}{3} x^{3}+7 x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 36
AsymptoticDSolveValue[(1-x^2)*y''[x]-8*x*y'[x]-12*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (7 x^5+\frac {10 x^3}{3}+x\right )+c_1 \left (15 x^4+6 x^2+1\right ) \]