12.13.29 problem 31(c)

Internal problem ID [1920]
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)
Date solved : Monday, January 27, 2025 at 05:38:25 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (4 x^{2}-4 x +1\right ) y^{\prime \prime }-\left (8-16 x \right ) y^{\prime }+8 y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 59

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);
 

\[ y = \left (-128 x^{5}-48 x^{4}-16 x^{3}-4 x^{2}+1\right ) y \left (0\right )+\left (80 x^{5}+32 x^{4}+12 x^{3}+4 x^{2}+x \right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 54

AsymptoticDSolveValue[(1-4*x+4*x^2)*D[y[x],{x,2}]-(8-16*x)*D[y[x],x]+8*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \left (-128 x^5-48 x^4-16 x^3-4 x^2+1\right )+c_2 \left (80 x^5+32 x^4+12 x^3+4 x^2+x\right ) \]