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The solution of (1 + y^(2)) dx = (Tan^(-...

The solution of `(1 + y^(2)) dx = (Tan^(-1) y -x) dy` is

A

`x e^(Tan^(-1)) y = (Tan^(-1) y -1) e^(Tan^(-1)y) + c`

B

`x e^(Tan^(-1)y) = (Tan^(-1) y -1) e^(Tan^(-1)y) -x + c`

C

`x = (Tan^(-1) y -1) e^(Tan^(-1)y) -y + c`

D

`x = (Tan^(-1) y + 1) e^(Tan^(-1)y) -x + y + c`

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

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  2. The solution of the differential equation y' = (1)/(e^(-y) - x), is

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

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  4. The solution of (1 + y^(2)) dx = (Tan^(-1) y -x) dy is

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

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  6. The solution of x (dy)/(dx) + y log y = xy e^(x) is

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  7. The solution of (dy)/(dx) = e^(x-y) (e^(x) - e^(y)) is

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  8. The solution of (dy)/(dx) + x sin 2y = x^(3) cos^(2) y is

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  9. The solution of cos y + (x sin y-1) (dy)/(dx) = 0 is

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  10. Solution of the differential equation cos x dy = y (sin x-y) dx, 0 lt ...

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  11. The solution of y'' + y' = 1 is

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  12. The solution of y'' = y' tan x = sin x is

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

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  14. x^(2) y -x^(3) (dy)/(dx) = y^(4) cos x rArr x^(3) y^(-3) =

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  15. The solution of the differential equation (1 + y^(2)) + (x- e^(Tan^(-1...

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  16. The solution of (dy)/(dx) = 1 -x(y-x) - x^(3) (y-x)^(3) is

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

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  18. The solution of 2y cos y^(2) (dy)/(dx) - (2)/(x +1) sin y^(2) = (x + 1...

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

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  20. If a curve y = f (x ) passes through the point (1 , -1) and satisfies...

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