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If x(dy)/(dx) = y (log y - log x +1), ...

If `x(dy)/(dx) = y (log y - log x +1)`, then the solution of the equation is

A

`y log ((x)/(y)) = cx`

B

`x log ((y)/(x)) = cy`

C

`log ((y)/(x)) = cx`

D

`log ((x)/(y)) = cy`

Text Solution

Verified by Experts

The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-DIFFERENTIAL EQUATIONS-Exercise 1
  1. The solution of (1 + e^(x//y)) dx + e^(x//y)(1-x//y) dy = 0 is

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

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  3. If x(dy)/(dx) = y (log y - log x +1), then the solution of the equat...

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  4. The solution of (12x + 5y -9) dx + (dx + 2y-4) dy = 0 is

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  5. The solution of (dy)/(dx) = (x-2y + 3)/(2x-y + 5) is

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  6. The solution of (dy)/(dx) = (x + y +1)/(x + y -1) is

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  7. Solve (dy)/(dx)=(x-2y+1)/(2x-4y)

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  8. The solution of the different equation (2x - 4y + 3)(dy)/(dx) + (x - 2...

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  9. The solution of (dy)/(dx) = (x + 7y + 2)/(3x + 5y + 6) is

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  10. Solve the following differential equations. (dy)/(dx)+(10x+8y-12)/(7...

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  11. The solution of (x + y +1) dx + (3x + 4y + 4) dy = 0 is

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  12. The solution of (3y -7x + 7) dx + (7y -3x + 3) dy = 0 is

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

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  14. Integrating factor of sin x (dy)/(dx) + y cos x = sin 2x is

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  15. Integrating factor of (dy)/(dx) + ((x sin x + cos x)/(xcosx) )y=1/(xc...

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  16. Integrating factor of (dy)/(dx) - (2)/(x +1) y = (x + 1)^(2) is

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  17. Integrating factor of the differential equation (1-x^(2)) (dy)/(dx) + ...

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

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

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

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