y'+2y=2-e^(-4t)

this is about as simple as they come.. my integrating factor is e^2t.. after multiplying through i can seperate into product rule, etc. but, when i integrate the right side there's that 2 there.. thats always going to yield a t term when integrated.. however the answer doesnt have that.. its

y(t) = C e^(-2 t)+e^(-4 t)/2+1

what happens to the t? or what am i doing wrong?

also, 1 more thing ( if youd be so kind), i got this example from

Pauls Online Notes : Differential Equations - Euler's Method
its the first example.. eulers wasnt too well went over in my class, and (apart from not understanding where the solution to initial problem comes from, which i really should know), im not positive how they go about getting the values for .2,.3, etc. i can follow his work to get .9 as the answer to .1, but he skips over hot to get the rest.. i dont see how the first can be a nice clean .9, but the rest are super long decimals. where does he go next?

really appreciate some quick help with this as i got a final coming up in a little more than 24 hours -_-