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Consider the family of all circles whose...

Consider the family of all circles whose centers lie on the straight line `y=x`. If the family of circles is represented by the differential equation `Py^('')+Qy^(')+1=0`, where P, Q are functions of x, y and `y^(')` (here `y^(')=(dy)/(dx),y^('')=(d^(2)y)/(dx^(2))`, then which of the following statements is (are) true?

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CENGAGE PUBLICATION-DIFFERENTIAL EQUATIONS-All Questions
  1. Let f:[1,oo) → [2, ∞) be a differentiable function such that f(1)=2...

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  2. If y(x) satisfies the differential equation y^(prime)-ytanx=2xs e c ...

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  3. Consider the family of all circles whose centers lie on the straight l...

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  4. Let y(x) be a solution of the differential equation (1+e^x)y^(prime)+y...

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  5. Let f be a real-valued differentiable function on R (the set of al...

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  6. The function y=f(x) is the solution of the differential equation (...

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  7. The order of the differential equation whose general solution is gi...

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  8. The differential equation representing the family of curves y^2=2c(x+s...

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  9. A curve y=f(x) passes through (1,1) and tangent at P(x , y) cuts t...

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  10. A curve is such that the mid-point of the portion of the tangent inter...

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  11. The equation of a curve passing through (2,7/2) and having gradien...

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  12. The equation of the curve which is such that the portion of the axi...

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  13. A normal at P(x , y) on a curve meets the x-axis at Q and N is t...

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  14. The differential equation of all non-horizontal lines in a plane is

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

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  16. The differential equation of the curve for which the initial ordina...

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

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  18. Which of the following is not the differential equation of family of c...

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  19. Tangent to a curve intercepts the y-axis at a point P .A line perpend...

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  20. The solution of the differential equation (xcoty+logcosx)dy+(logsiny-y...

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