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Find the particular solution of `(cos x – x sin x +y^2)dx + 2xy dy = 0` that satisfies the initial condition y = 1 when x = `pi`

A

`xy^2 + xcos x` = 0

B

`xy^2 - xcos x` = 0

C

`xy^2 + xsin x = 0`

D

`x^2Y + xsin x = 0`

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The correct Answer is:
A
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MOTION-DIFFERENTIAL EQUATION -Exercise 2
  1. Solution of the equation (1 - x^2) dy + xy dx = xy^2dx is

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. Which one of the following is homogeneous function ?

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

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

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  18. The equation of the curve passing through (3,4) and satisfying the dif...

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  19. The orthogonal trajectories of the system of curves y^2 =cx^3 are

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  20. The solution the differential equation (dy/dx)^2 - (dy/dx)(e^x+e^(-x))...

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