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If y = y (x) is the solution of the diff...

If y = y (x) is the solution of the differential equation `((2 + sin x)/(y + 1)) (dy)/(dx) + cos x = 0` with y(0) = 1 then `y ((pi)/(2))`=

A

`(1)/(3)`

B

`(2)/(3)`

C

1

D

`(4)/(3)`

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The correct Answer is:
A
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DIPTI PUBLICATION ( AP EAMET)-DIFFERENTIAL EQUATIONS-Exercise 1
  1. The solution of (dy)/(dx) = e^(2x-y) + x^(3) e^(-y) is

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

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

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

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  5. The solution of (e^(x) + 1) y dy + (y+ 1) dx = 0 is

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  6. The solution of e^(x) tan y dx + (1- e^(x)) sec^(2) y dy = 0 is

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  7. The solution of 3e^(x) cos^(2) y dx + (1 + e^(x)) cot y dy = 0 is

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  8. The solution of y dx - x dy + 3x^(2) y^(2) e^(x) dx = 0 is

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

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  10. The solution of (xy^(2) + x) dx + (yx^(2) + y) dy = 0 is

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  11. The solution of xdx + ydy = x^(2) y dy - xy^(2) dx is

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  12. The solution of (dy)/(dx) = 2xy - 2y + 2x -3 is

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  13. The solution of (dy)/(dx) + (x (1+y^(3)))/(y^(2) (1 + x^(2))) = 0 is

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  14. The solution of (1 -x^(2)) (dy)/(dx) + xy = 5x is

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  15. The solution of (x^(2) y^(3) + x^(2)) + (y^(2) x^(3) + y^(2)) dy = 0 ...

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  16. The solution of the differential equation ydx + (x + x^(2)y) dy = 0 is

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  17. dx + dy = (x + y) (dx -dy) rArr log (x + y) =

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  18. The solution of the differenital equation (dy)/(dx) = (x +y)/(x) satis...

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  19. The solution of (dy)/(dx) + 1 = e^(x + y) is

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

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