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

Options

A. `A + B = 0`
B. `A + B = 12`
C. `|AB| = 36`
D. `|AB| = 49`

Answer

A, C

Explanation

`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.