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Let the popultion of rabbits surviving a...

Let the popultion of rabbits surviving at a time t be governed by the differential equation `(dp(t))/(dt) = (1)/(2) p (t) - 200`. If p(0) = 100, the p(t) equals

A

`600-500 e^(1//2)`

B

`400 - 300 e^(-1//2)`

C

`400 - 300 e^(1//2)`

D

`300 - 200 e^(-1//2)`

Text Solution

Verified by Experts

The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-DIFFERENTIAL EQUATIONS-Exercise 1
  1. The population P(t) at time t of a certain mouse species satisfies the...

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  2. At present, a firm is manufacturing 2000 items. It is estimated that t...

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  3. Let the popultion of rabbits surviving at a time t be governed by the ...

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  4. If (dy)/(dx) = y + 3 gt 0 and y(0) =2, then y (ln 2) is equal to :

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  5. The solution of x^(2) + y^(2) (dy)/(dx) =4 is

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  6. The solution of 2xy (dy)/(dx) =1 + y^(2) is

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  7. The general solution of (dy)/(dx) + (sqrt(1 - y^(2)))/(sqrt(1 - x^(2))...

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  8. The solution of x^(2) (dy)/(dx) = sqrt(4 - y^(2)) is

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  9. The general solution of (dy)/(dx) + (sqrt(1 - y^(2)))/(sqrt(1 - x^(2))...

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  10. The general solution of x sqrt(1 + y^(2)) dx + y sqrt(1 + x^(2)) dy = ...

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  11. The solution of x sqrt(1 - y^(2)) dx + y sqrt(1 - x^(2)) dy = 0 is

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  12. The solution of sqrt(1 + x^(2)) dx + sqrt(1 + y^(2)) dy = 0 is

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  13. The solution of (dy)/(dx) + (y^(2) + y +1)/(x^(2) + x + 1) = 0 is

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  14. The solution of the differential equation (dy)/(dx) = (xy + y)/(yx + x...

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  15. The solution of (dy)/(dx) = (x + x^(2))/(y + y^(2)) is

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  16. The solution of e^(x-y) dx + e^(y-x) dy = 0 is

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  17. The solution of (dy)/(dx) = e^(2x-y) + x^(3) e^(-y) is

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  18. The general solution of tanysec^(2) x dx + tan x sec^(2) y dy = 0 is

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  19. If y = y (x) is the solution of the differential equation ((2 + sin x)...

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  20. The solution of e^(x) cot y dx + (1- e^(x)) cosec^(2) y dy = 0 is

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