Solve the initial value problem $$(2 + x^2)y'' + 3 y = 0, \,y(0) = 0, \,y'(0) = 4 .$$ If the solution is

$y = c_0 + c_1 x + c_2 x^2 + c_3 x^3 + c_4 x^4 + c_5 x^5 + c_6 x^6 + c_7 x^7 + \cdots$ ,

enter the following coefficients:

$c_0 =$
$c_1 =$
$c_2 =$
$c_3 =$
$c_4 =$
$c_5 =$
$c_6 =$
$c_7 =$