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The solution of differential equation ...

The solution of differential equation
`(1+y^(2))+(x-e^(tan^(-1)y))(dy)/(dx)=0`, is

A

`x e^(2tan^-1y) = e^(tan^-1y) +k`

B

`(x-2) = k(e^-(tan^-1)y)`

C

`2xe^(tan^-1y) =e^(2tan^-1y) +K`

D

`x (e^(tan^-1)y) = tan^-1 y+k`

Text Solution

Verified by Experts

The correct Answer is:
C
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MOTION-DIFFERENTIAL EQUATION -Exercise 2
  1. The general solution of the differential equation (dy)/(dx)+(1+cos2y)/...

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  2. The solution of the differential equation (dy)/(dx)=(xy)/(x^2+y^2) is

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  3. The solution of differential equation (1+y^(2))+(x-e^(tan^(-1)y))(dy...

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  4. The solution of the differential equation, e^x(x +1)dx + (ye^y -xe^x)d...

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

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  6. The solution of the differential equation x^2(dy)/(dx)cos1/x-ysin1/x=-...

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  7. The solution of (dy)/(dx) + y tan x = sec x is

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  8. Solution of the differential equation (dy)/(dx)+ytanx=x^(n)cosx is

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  9. (dy)/(dx)+(3x^2)/(1+x^3)y=(sin^2x)/(1+x^3)

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  10. Solution of the equation (1 - x^2) dy + xy dx = xy^2dx is

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  11. Solve the differential equation (y^2+x^2)dx=(x^2+xy)dy

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  12. Find the particular solution of (cos x – x sin x +y^2)dx + 2xy dy = 0 ...

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  13. Orthogonal trajectories of family of the curve x^(2/3)+y^2/3=a^((2/3))...

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  14. The curve in the first quadrant for which the normal at any point (...

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  15. A curve C passes through origin and has the property that at each poin...

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  16. Water is drained from a vertical cylindrical tank by opening a valv...

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  17. If y=x/(In|cx|) (where c is an arbitrary constant) is the general solu...

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  18. Number of straight lines which satisfy the differential equation (dy)/...

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  19. If f''(x)+f'(x)+f^(2)(x)=x^(2) be the differentiable equation of a cur...

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  20. If y= e^((k+1)x) is a solution of differential equation (d^2y)/(dx^2) ...

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