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If y(t) satisfies the differential equat...

If y(t) satisfies the differential equation `y'(t)+2y(t)=2e^(-2t),y(0)=2` then y(1) equals

A

`(3)/(e)`

B

`(3)/(e^(2))`

C

`(4)/(e)`

D

`(4)/(e^(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
`y'(t) + 2y(t) = 2e^(2t)` is linear differential equation
I.F. = `e^(2t)`
`therefore" ""solution is y" e^(2t) = 2t + C`
Given y(0) = 2
`rArr" "2 = C`
`rArr" "ye^(2t)=2(t+1)`
When t = 1, `y(1)=(4)/(e^(2))`
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