Solve the differential equation below using series methods:

$y^{\text{'}\text{'}}-e^{x}y=0,y(0)=3,y^{\text{'}}(0)=2$

The first few terms of the series solution $y={\displaystyle \underset{k=0}{\overset{}{}}}{a}_k{x}^k$ are

$a_0=$

$a_1=$

$a_2=$

$a_3=$

$a_4=$