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

The solution of `(dy)/(dx) + (3x^(2) y)/(1 + x^(3)) = (sin^(2) x)/(1 + x^(3))` is

A

`2y (1 + x^(3)) = x + sin x cos x + c`

B

`2y (1 -x^(3)) = x + sin x cos x + c`

C

`2y (1 + x^(3)) = x - sin x cos x + c`

D

`2y (1-x^(3)) = x - sin x cos x + c`

Text Solution

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The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-DIFFERENTIAL EQUATIONS-Exercise 1
  1. Integrating factor of the differential equation (1-x^(2)) (dy)/(dx) + ...

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  2. An integrating factor of the equation (1 + y + x^(2)y) dx + (x + x^(3)...

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

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

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  5. The solution of (x^(2) + 1) (dy)/(dx) + 4xy = (1)/(x^(2) + 1) is

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  6. The solution of (1 + x^(2)) (dy)/(dx) + 2xy - 4x^(2) = 0 is

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

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

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  9. The solution of the differential equation (dy)/(dx) - 2y tan 2x = e^(x...

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

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  11. Solve the following differential equations. x(x-1)(dy)/(dx)-(x-2)y=x...

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

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

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

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

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

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

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  18. The solution of cos x(dy)/(dx) + y = sin x is

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  19. The solution of (dy)/(dx) + y cos x = sin x cos x is

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

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