Internal problem ID [14800]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.8, page 203
Problem number: 24 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Gegenbauer, [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +9 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
Order:=6; dsolve((1-x^2)*diff(y(x),x$2)-x*diff(y(x),x)+9*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-\frac {9}{2} x^{2}+\frac {15}{8} x^{4}\right ) y \left (0\right )+\left (x -\frac {4}{3} x^{3}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 35
AsymptoticDSolveValue[(1-x^2)*y''[x]-x*y'[x]+9*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (x-\frac {4 x^3}{3}\right )+c_1 \left (\frac {15 x^4}{8}-\frac {9 x^2}{2}+1\right ) \]