Internal problem ID [1220]
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: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (2 x^{2}-4 x +1\right ) y^{\prime \prime }+10 \left (x -1\right ) y^{\prime }+6 y=0} \end {gather*} With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
Order:=6; dsolve((1-4*x+2*x^2)*diff(y(x),x$2)+10*(x-1)*diff(y(x),x)+6*y(x)=0,y(x),type='series',x=1);
\[ y \relax (x ) = \left (1+3 \left (x -1\right )^{2}+\frac {15 \left (x -1\right )^{4}}{2}\right ) y \relax (1)+\left (x -1+\frac {8 \left (x -1\right )^{3}}{3}+\frac {32 \left (x -1\right )^{5}}{5}\right ) D\relax (y )\relax (1)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 49
AsymptoticDSolveValue[(1-4*x+2*x^2)*y''[x]+10*(x-1)*y'[x]+6*y[x]==0,y[x],{x,1,5}]
\[ y(x)\to c_1 \left (\frac {15}{2} (x-1)^4+3 (x-1)^2+1\right )+c_2 \left (\frac {32}{5} (x-1)^5+\frac {8}{3} (x-1)^3+x-1\right ) \]