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The solution of x (dy)/(dx) = y + xe^(y/...

The solution of `x (dy)/(dx) = y + xe^(y//x) " with " y(1) = 0` is

A

`e^(-y//x) m log x`

B

`e^(-y//x) + 2 log x = 1`

C

`e^(-y//x) + log x = 1`

D

`e^(y//x) + log x = 1`

Text Solution

Verified by Experts

The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-DIFFERENTIAL EQUATIONS-Exercise 1
  1. Solve : x dy= (y+x " cos"^(2)(y)/(x))dx

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  2. Solve : x " sin"(y)/(x).(dy)/(dx)=y " sin"(y)/(x)-x

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  3. The solution of x (dy)/(dx) = y + xe^(y//x) " with " y(1) = 0 is

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  4. The solution of the differential equation xy' = 2xe^(-y//x) + y is

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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