Variation of parameters differential equation with exponentials

[xlzhsteven]

Question is attached as Clipboard01.jpg

I have tried the use Variation of Parameters to solve this question, but I kept getting wrong answer.
This is What I get y=(2e^x)(Cos(e^x))+0.5(e^(-x))Cos(e^(-x))-2Sin(e^(-x))
This is the right answer: y=-Sin(e^(-x))-(e^x)Cos(e^(-x))

Procedure is shown in the second jpg file
Can someone help me with this problem?
Thank You

 

[HallsofIvy]

Show how you got that answer and we will try to help.

 

[xlzhsteven]

I have attached my procedure in scan0002.jpg

 

[xlzhsteven]

Can anyone help me? I have math final tomorrow.