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The differential equation of family of curves whose tangent form an angle of `pi/4` with the hyperbola `xy=C^2` is

A

`(dy)/(dx) = (x^2 + C^(2))/(x^2 - C^(2)) `

B

`(dy)/(dx) = (x^(2) - C^(2))/(x^(2) + C^(2)) `

C

`(dy)/(dx) = -(C^2)/(x^2`

D

None of these

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The correct Answer is:
B
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DISHA PUBLICATION-DIFFERENTIAL EQUATIONS -Exercise-2 : Concept Applicator
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  5. A ray of light coming from origin after reflectiion at the point P (x ...

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  7. If y=(x+sqrt(1+x^2))^n then (1+x^2)(d^2y)/(dx^2)+x(dy)/(dx)

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  8. The solution of differential equation x y^(prime)=x((y^2)/(x^2)+(f((y^...

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  9. The solution of the differential equation (dy)/(dx)=(1-3y-3x)/(1+x+y) ...

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  10. The solution of the equation (dy)/(dx)=((y^(2) -y-2))/(x^(2) + 2x+3) i...

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  11. The solution of differential equation (dy)/(dx) = e^(x-y) + x^(2)e^(-y...

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  12. Let f be a non-negative function defined on the interval [0,1]. If int...

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  13. Solution of the differential equation (1+e^(x/y))dx + e^(x/y)(1-x/y)dy...

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  14. In a culture, the bacteria count is 1,00,000. The number is increas...

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  15. The solution of the differential equation (dy)/(dx)=(4x+y+1)^(2), is

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  16. The solution of the differential equation x^(3)(dy)/(dx)+4x^(2) tany=e...

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  17. Solution of the differential equation ((x+y-1)/(x+y-2))(dy)/(dx)=((x+y...

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  18. Solve (1+e^((x)/(y)))dx + e^((x)/(y)) (1-(x)/(y))dy = 0

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

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