Internal problem ID [4398]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 12, Series Solutions of Differential Equations. Section 1. Miscellaneous problems. page
564
Problem number: 8, using series method.
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 \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 28
Order:=6; dsolve((x^2+2*x)*diff(y(x),x$2)-2*(x+1)*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+\mathrm {O}\left (x^{6}\right )\right ) c_{1} x^{2}+c_{2} \left (-2-2 x -\frac {1}{2} x^{2}+\mathrm {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.07 (sec). Leaf size: 23
AsymptoticDSolveValue[(x^2+2*x)*y''[x]-2*(x+1)*y'[x]+2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 x^2+c_1 \left (\frac {x^2}{4}+x+1\right ) \]