Internal problem ID [717]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 5.2, Series Solutions Near an Ordinary Point, Part I. page 263
Problem number: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime \prime }-4 y^{\prime } x +6 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: 25
Order:=6; dsolve((1+x^2)*diff(y(x),x$2)-4*x*diff(y(x),x)+6*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = y \relax (0)+D\relax (y )\relax (0) x -3 y \relax (0) x^{2}-\frac {D\relax (y )\relax (0) x^{3}}{3} \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 26
AsymptoticDSolveValue[(1+x^2)*y''[x]-4*x*y'[x]+6*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (x-\frac {x^3}{3}\right )+c_1 \left (1-3 x^2\right ) \]