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The general solution of e^(y)((dy)/(dx))...

The general solution of `e^(y)((dy)/(dx)) + 2(e^(y))/(x) = Sin x` is

A

`x e^(y) = -x Cos x + Sin x + c`

B

`x^(2) e^(y) = -x^(2) Cos x + 2x Sin x - Cos x + c`

C

`x e^(y) = x Cos x - Sin x + c`

D

`e^(y) = -Cos x + (2 Sin x)/(x) + (2 Cos x)/(x^(2)) + (c)/(x^(2))`

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The correct Answer is:
D
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AAKASH SERIES-DIFFERENTIAL EQUATIONS-Exercise - II
  1. The solution of (1)/(x)(dy)/(dx) + y e^(x) = e^((1-x)^(e^(x))) is

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  2. Which of the following statement is correct ? Statement I if dy+2xyd...

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

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  4. Solution of xy - (dy)/(dx) = y^(3)e^(-x^(2)) is

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  5. Solve (dy)/(dx) + (y)/(x) = x^(2)y^(6)

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

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

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  8. If x^(2)y-x^(3)(dy)/(dx)=y^(4)cosx then x^(3)y^(-3) is equal to

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  9. Match the differential equations in List-I to their integrating factor...

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  10. The solution of (dx)/(dy) - (2)/(3)xy = x^(4)y^(3) is

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  11. If the solution of cosec^(2)x(dy)/(dx) - (1)/(y) = 0 is ax + b sin 2x ...

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  12. Assertion (A) : Integrating factor of 1+(x tan y - sec)(dy)/(dx) = 0 i...

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  13. Assertion (A) : The differential equaiton of the family of rectangular...

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  14. Asserton (A) : The solution of (dy)/(dx) = (x+y)/(x) is e^(y//x) = cx ...

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

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  16. An integrating factor of the equation (1+y+x^(2)y)dx+(x+x^(3))dy=0 is

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  17. The solution of the differential equation (dy)/(dx) + (y)/(2) sec x = ...

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  18. The differential equation of co-axial system of circles x^(2) + y^(2) ...

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  19. The trajectories orthogonal to x^(2)+y^(2) = 2ax is

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  20. The volume of spherical ballon being inflated changes at a constant ra...

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