Internal problem ID [4512]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 8, Series solutions of differential equations. Section 8.4. page 449
Problem number: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Hermite]
Solve \begin {gather*} \boxed {y^{\prime \prime }-x y^{\prime }-3 y=0} \end {gather*} With the expansion point for the power series method at \(x = 2\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 50
Order:=6; dsolve(diff(y(x),x$2)-x*diff(y(x),x)-3*y(x)=0,y(x),type='series',x=2);
\[ y \relax (x ) = \left (1+\frac {3 \left (x -2\right )^{2}}{2}+\left (x -2\right )^{3}+\frac {9 \left (x -2\right )^{4}}{8}+\frac {3 \left (x -2\right )^{5}}{4}\right ) y \relax (2)+\left (x -2+\left (x -2\right )^{2}+\frac {4 \left (x -2\right )^{3}}{3}+\frac {13 \left (x -2\right )^{4}}{12}+\frac {5 \left (x -2\right )^{5}}{6}\right ) D\relax (y )\relax (2)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 79
AsymptoticDSolveValue[y''[x]-x*y'[x]-3*y[x]==0,y[x],{x,2,5}]
\[ y(x)\to c_1 \left (\frac {3}{4} (x-2)^5+\frac {9}{8} (x-2)^4+(x-2)^3+\frac {3}{2} (x-2)^2+1\right )+c_2 \left (\frac {5}{6} (x-2)^5+\frac {13}{12} (x-2)^4+\frac {4}{3} (x-2)^3+(x-2)^2+x-2\right ) \]