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A curve passes through the point (0,1) a...

A curve passes through the point (0,1) and the gradient at (x,y) on it is `y(xy-1)`. The equation of the curve is

A

`y(x-1)=1`

B

`y(x+1)=1`

C

`x(y+1)=1`

D

`x(y-1)=1`

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The correct Answer is:
B
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OBJECTIVE RD SHARMA-DIFFERENTIAL EQUATIONS-Exercise
  1. The solution of the differential equation (dy)/(dx)+(y)/(x)=x^(2), is

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

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  3. Solution of x(dy)/(dx)+y=xe^(x), is

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  4. The tangent at any point (x , y) of a curve makes an angle tan^(-1)(2x...

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  5. The integrating factor of the differential equation (dy)/(dx)+y=(1+y)/...

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  6. The degree of the differential equation corresponding to the family of...

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  7. The degree of the differential equation of all curves having normal of...

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  8. The differential equation of the family of ellipses having major and m...

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  9. The degree of the differential equation satisfying the relation sqrt(1...

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  10. The differential eqaution of the family of curve y^(2)=4a(x+1), is

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  11. Find the equation of the curve in which the subnormal varies as the ...

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  12. Solution of the differential equation xdy-ydx=0 represents

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  13. The equation of the curve whose subnormal is twice the abscissa, is

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

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  15. A curve passes through the point (0,1) and the gradient at (x,y) on it...

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  16. The equation of the curve through the point (1,0), whose slope is (y-...

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  17. The differential equation for which sin^(-1) x + sin^(-1) y = c is giv...

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  18. Solution of the differential equation (dx)/(x)+(dy)/(y)=0 is

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  19. The order of the differential equation of family of circles touching t...

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  20. The function f(x) satisfying the equation f^2 (x) + 4 f'(x) f(x) + (...

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