Finding Wronskian with Given Initial Conditions for Non-Homogeneous ODE

[ehhh]

Homework Statement

Suppose the Wronskian of W(y1, y2) [0] = 1
y1, y2 are solutions to the differential: y'' + e^xy'+ tanx = 0
Find W(y1, y2)[1] ?

The Attempt at a Solution

So I'm thinking of using Abel's theorem, where p(x) = e^x
W(y1, y2)(0) = = c e^{\int{- e^t dt}}
So, 1 = ce^{e^{-t}}
But I'm not too sure what to do now..

I then tried to find out what y1, y2 were so I could just calculate W directly at x = 1.
Since it's not homogeneous (the tanx term) I was thinking of using variations of parameters. But I the e^x term doesn't allow me to find the characteristic equation to find that..

 

[ehhh]

I think the answer of it was e^(e - 1) but I'm not too sure if it's correct