Internal problem ID [1221]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.2 SERIES SOLUTIONS NEAR AN
ORDINARY POINT I. Exercises 7.2. Page 329
Problem number: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (2 x^{2}-8 x +11\right ) y^{\prime \prime }-16 \left (-2+x \right ) y^{\prime }+36 y=0} \end {gather*} With the expansion point for the power series method at \(x = 2\).
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 29
Order:=6; dsolve((11-8*x+2*x^2)*diff(y(x),x$2)-16*(x-2)*diff(y(x),x)+36*y(x)=0,y(x),type='series',x=2);
\[ y \relax (x ) = \left (1-6 \left (-2+x \right )^{2}+\frac {4 \left (-2+x \right )^{4}}{3}\right ) y \relax (2)+\left (-2+x -\frac {10 \left (-2+x \right )^{3}}{9}\right ) D\relax (y )\relax (2)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 40
AsymptoticDSolveValue[(11-8*x+2*x^2)*y''[x]-16*(x-2)*y'[x]+36*y[x]==0,y[x],{x,2,5}]
\[ y(x)\to c_1 \left (\frac {4}{3} (x-2)^4-6 (x-2)^2+1\right )+c_2 \left (-\frac {10}{9} (x-2)^3+x-2\right ) \]