Find two linearly independent solutions of $2x^2y'' -xy' + (-4 x + 1)y = 0, \, x>0$
of the form

$y_1 = x^{r_1}(1 + a_1 x + a_2 x^2 + a_3 x^3 + \cdots)$

$y_2 = x^{r_2}(1 + b_1 x + b_2 x^2 + b_3 x^3 + \cdots)$

where $r_1 > r_2.$

Enter

$r_1 =$
$a_1 =$
$a_2 =$
$a_3 =$

$r_2 =$
$b_1 =$
$b_2 =$
$b_3 =$