Internal problem ID [1270]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.3 SERIES SOLUTIONS NEAR AN
ORDINARY POINT II. Exercises 7.3. Page 338
Problem number: 31(c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {\left (4 x^{2}-4 x +1\right ) y^{\prime \prime }-\left (8-16 x \right ) y^{\prime }+8 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 54
Order:=6; dsolve((1-4*x+4*x^2)*diff(y(x),x$2)-(8-16*x)*diff(y(x),x)+8*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (-128 x^{5}-48 x^{4}-16 x^{3}-4 x^{2}+1\right ) y \relax (0)+\left (80 x^{5}+32 x^{4}+12 x^{3}+4 x^{2}+x \right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 54
AsymptoticDSolveValue[(1-4*x+4*x^2)*y''[x]-(8-16*x)*y'[x]+8*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-128 x^5-48 x^4-16 x^3-4 x^2+1\right )+c_2 \left (80 x^5+32 x^4+12 x^3+4 x^2+x\right ) \]