Internal problem ID [4511]
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: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x +1\right ) y^{\prime \prime }-3 x y^{\prime }+2 y=0} \end {gather*} With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 54
Order:=6; dsolve((x+1)*diff(y(x),x$2)-3*x*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=1);
\[ y \relax (x ) = \left (1-\frac {\left (x -1\right )^{2}}{2}-\frac {\left (x -1\right )^{3}}{6}-\frac {5 \left (x -1\right )^{4}}{48}-\frac {7 \left (x -1\right )^{5}}{240}\right ) y \relax (1)+\left (x -1+\frac {3 \left (x -1\right )^{2}}{4}+\frac {\left (x -1\right )^{3}}{3}+\frac {\left (x -1\right )^{4}}{6}+\frac {7 \left (x -1\right )^{5}}{120}\right ) D\relax (y )\relax (1)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 87
AsymptoticDSolveValue[(x+1)*y''[x]-3*x*y'[x]+2*y[x]==0,y[x],{x,1,5}]
\[ y(x)\to c_1 \left (-\frac {7}{240} (x-1)^5-\frac {5}{48} (x-1)^4-\frac {1}{6} (x-1)^3-\frac {1}{2} (x-1)^2+1\right )+c_2 \left (\frac {7}{120} (x-1)^5+\frac {1}{6} (x-1)^4+\frac {1}{3} (x-1)^3+\frac {3}{4} (x-1)^2+x-1\right ) \]