Internal problem ID [719]
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: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (-x^{2}+3\right ) y^{\prime \prime }-3 y^{\prime } x -y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
Order:=6; dsolve((3-x^2)*diff(y(x),x$2)-3*x*diff(y(x),x)-y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+\frac {1}{6} x^{2}+\frac {1}{24} x^{4}\right ) y \relax (0)+\left (x +\frac {2}{9} x^{3}+\frac {8}{135} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 70
AsymptoticDSolveValue[(3-x^2)*y''[x]-3*y'[x]-y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {13 x^5}{1080}+\frac {x^4}{36}+\frac {x^3}{18}+\frac {x^2}{6}+1\right )+c_2 \left (\frac {49 x^5}{1080}+\frac {7 x^4}{72}+\frac {2 x^3}{9}+\frac {x^2}{2}+x\right ) \]