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

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

A

`y(1+x^3) =x +1/2sin2x +c`

B

`y (1+x^3) = cx +1/2 sin 2x`

C

`y(1+x^3) =cx -1/2 sin 2x`

D

`y (1+x^3) =x/2- 1/4 sin2x +c`

Text Solution

Verified by Experts

The correct Answer is:
D
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MOTION-DIFFERENTIAL EQUATION -Exercise 2
  1. The solution of (dy)/(dx) + y tan x = sec x is

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. The differential equation (d^2y)/dx^2+x dy/dx+siny+x^2=0, is which of...

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  16. Let y = (A + Bx) e^(3x) is a solution of the differential equation(d^2...

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  17. y=a e^(-1/x)+b is a solution of (dy)/(dx)=y/(x^2), then (a) ( b ...

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  18. Which one of the following is homogeneous function ?

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  19. The graph of the function y = f(x) passing through the point (0, 1) an...

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  20. (x^2y^3+xy)dy=dx

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