Internal problem ID [740]
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 \(x_0=4\) only.
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: 0.004 (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);
\[ y \relax (x ) = \left (1-\frac {2 \left (x -4\right )^{2}}{5}+\frac {4 \left (x -4\right )^{3}}{15}-\frac {4 \left (x -4\right )^{4}}{25}+\frac {199 \left (x -4\right )^{5}}{1875}\right ) y \relax (4)+\left (x -4-\frac {2 \left (x -4\right )^{2}}{5}+\frac {\left (x -4\right )^{3}}{10}-\frac {2 \left (x -4\right )^{4}}{75}+\frac {157 \left (x -4\right )^{5}}{15000}\right ) D\relax (y )\relax (4)+O\left (x^{6}\right ) \]
✓ 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}]
\[ y(x)\to c_1 \left (\frac {199 (x-4)^5}{1875}-\frac {4}{25} (x-4)^4+\frac {4}{15} (x-4)^3-\frac {2}{5} (x-4)^2+1\right )+c_2 \left (\frac {157 (x-4)^5}{15000}-\frac {2}{75} (x-4)^4+\frac {1}{10} (x-4)^3-\frac {2}{5} (x-4)^2+x-4\right ) \]