Internal problem ID [743]
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: 7. case \(x_0=2\).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{3}+1\right ) y^{\prime \prime }+4 y^{\prime } x +y=0} \end {gather*} With the expansion point for the power series method at \(x = 2\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 54
Order:=6; dsolve((1+x^3)*diff(y(x),x$2)+4*x*diff(y(x),x)+y(x)=0,y(x),type='series',x=2);
\[ y \relax (x ) = \left (1-\frac {\left (-2+x \right )^{2}}{18}+\frac {10 \left (-2+x \right )^{3}}{243}-\frac {451 \left (-2+x \right )^{4}}{17496}+\frac {1151 \left (-2+x \right )^{5}}{78732}\right ) y \relax (2)+\left (-2+x -\frac {4 \left (-2+x \right )^{2}}{9}+\frac {115 \left (-2+x \right )^{3}}{486}-\frac {271 \left (-2+x \right )^{4}}{2187}+\frac {9713 \left (-2+x \right )^{5}}{157464}\right ) D\relax (y )\relax (2)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 87
AsymptoticDSolveValue[(1+x^3)*y''[x]+4*x*y'[x]+y[x]==0,y[x],{x,2,5}]
\[ y(x)\to c_1 \left (\frac {1151 (x-2)^5}{78732}-\frac {451 (x-2)^4}{17496}+\frac {10}{243} (x-2)^3-\frac {1}{18} (x-2)^2+1\right )+c_2 \left (\frac {9713 (x-2)^5}{157464}-\frac {271 (x-2)^4}{2187}+\frac {115}{486} (x-2)^3-\frac {4}{9} (x-2)^2+x-2\right ) \]