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Let x=x(t) and y=y(t) be solutions of th...

Let `x=x(t)` and `y=y(t)` be solutions of the differential equations `(dx)/(dt)+ax=0` and `(dy)/(dt)+by=0]`, respectively,`a,b in R` .Given that `x(0)=2,y(0)=1` and `3y(1)=2x(1)` ,the value of "t" ,for which, `[x(t)=y(t)` ,is :

A

`log_(3)4`

B

`log_(4)3`

C

`log_((4)/(3))2`

D

`log_((2)/(3))2`

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Knowledge Check

  • If x = 3t , y = (1)/(2) ( t + 1) , then the value of t for which x = 2y is

    A
    A)1
    B
    B)`(1)/(2)`
    C
    C)`-1`
    D
    D)`(2)/(3)`

  • Let Y = y(x) be the solution of the differential equation ( dy ) /( dx) + 2y = f(x) , where f(x) = { {:(1, x in [0,1]),( 0, " Otherwise "):} IF y(0) =0 then y ((3)/(2)) is :

    A
    ` ( e^2-1)/( 2e ^3)`
    B
    ` ( e^2-1)/(e^3)`
    C
    `(e ^2 +1)/( 2e ^4)`
    D
    `(1)/(2e)`

  • 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`

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