Internal problem ID [2467]
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. Additional problems. Section
11.7. page 788
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (1-x^{2}\right ) y^{\prime \prime }-6 y^{\prime } x -4 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)-6*x*diff(y(x),x)-4*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (3 x^{4}+2 x^{2}+1\right ) y \relax (0)+\left (x +\frac {5}{3} x^{3}+\frac {7}{3} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 38
AsymptoticDSolveValue[(1-x^2)*y''[x]-6*x*y'[x]-4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {7 x^5}{3}+\frac {5 x^3}{3}+x\right )+c_1 \left (3 x^4+2 x^2+1\right ) \]