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If the solution of the equation (d^(2)x)...

If the solution of the equation `(d^(2)x)/(dt^(2))+4(dx)/(dt)+3x = 0` given that for `t = 0, x = 0 and (dx)/(dt) = 12` is in the form `x = Ae^(-3t) + Be^(-t)`, then

A

`A + B = 0`

B

`A + B = 12`

C

`|AB| = 36`

D

`|AB| = 49`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`x = Ae^(-3t) + Be^(-t)`
`therefore" "(dx)/(dt)= -3Ae^(-3t) - Be^(-t)`
When t = 0, x = 0
`therefore" "A + B = 0" "(i)`
At t = 0, `(dx)/(dt) = 12`
`therefore" "12 = -3A - B" "(ii)`
Solving, we get A = -6, B = 6.
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