Internal problem ID [718]
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: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (-x^{2}+4\right ) y^{\prime \prime }+2 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: 29
Order:=6; dsolve((4-x^2)*diff(y(x),x$2)+2*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (-\frac {x^{2}}{4}+1\right ) y \relax (0)+\left (x -\frac {1}{12} x^{3}-\frac {1}{240} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 35
AsymptoticDSolveValue[(4-x^2)*y''[x]+2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (1-\frac {x^2}{4}\right )+c_2 \left (-\frac {x^5}{240}-\frac {x^3}{12}+x\right ) \]