Internal problem ID [741]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 5.3, Series Solutions Near an Ordinary Point, Part II. page 269
Problem number: 6. case \(x_0=-4\).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}-2 x -3\right ) y^{\prime \prime }+y^{\prime } x +4 y=0} \end {gather*} With the expansion point for the power series method at \(x = -4\).
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 54
Order:=6; dsolve((x^2-2*x-3)*diff(y(x),x$2)+x*diff(y(x),x)+4*y(x)=0,y(x),type='series',x=-4);
\[ y \relax (x ) = \left (1-\frac {2 \left (x +4\right )^{2}}{21}-\frac {4 \left (x +4\right )^{3}}{189}-\frac {4 \left (x +4\right )^{4}}{1323}-\frac {\left (x +4\right )^{5}}{3087}\right ) y \left (-4\right )+\left (x +4+\frac {2 \left (x +4\right )^{2}}{21}-\frac {\left (x +4\right )^{3}}{54}-\frac {11 \left (x +4\right )^{4}}{1323}-\frac {157 \left (x +4\right )^{5}}{74088}\right ) D\relax (y )\left (-4\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 87
AsymptoticDSolveValue[(x^2-2*x-3)*y''[x]+x*y'[x]+4*y[x]==0,y[x],{x,-4,5}]
\[ y(x)\to c_1 \left (-\frac {(x+4)^5}{3087}-\frac {4 (x+4)^4}{1323}-\frac {4}{189} (x+4)^3-\frac {2}{21} (x+4)^2+1\right )+c_2 \left (-\frac {157 (x+4)^5}{74088}-\frac {11 (x+4)^4}{1323}-\frac {1}{54} (x+4)^3+\frac {2}{21} (x+4)^2+x+4\right ) \]