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Find the equation of a curve such that t...

Find the equation of a curve such that the projection of its ordinate upon the normal is equal to its abscissa.

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The correct Answer is:
`y^2 +- y sqrt(y^2-x^2)/x^2 = ln |(y +- sqrt(y^2-x^2), c^2/x^3|`, where same sign has to be taken
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MOTION-DIFFERENTIAL EQUATION -Exercise 3
  1. Find the curve for which the sum of the lengths of the tangent and sub...

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  2. Find the curve y= f(x) where f(X) ge 0, f(0) =0,bounding a curvilinear...

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  3. Find the equation of a curve such that the projection of its ordinate ...

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  4. The light rays emanating from a point source situated at origin when r...

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  5. The perpendicular from the origin to the tangent at any point on a cur...

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  6. Find the curve for which any tangent intersects the y-axis at the poin...

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  7. Find the curve such that the area of the trapezium formed by the co-or...

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  8. Find the equation of the curve passing through the origin if the middl...

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  9. A perpendicular drawn from any point P of the curve on the x-axis meet...

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  10. The equation of curve in which portion of y-axis cutoff between origin...

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  11. Find the orthogonal trajectories for the given family of curves when ‘...

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  12. The population P of a town decreases at a rate proportional to the num...

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  13. It is known that the decay rate of radium is directly proportional to ...

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  14. Let the function ln f(x) is defined where f(x) exists for x geq 2 an...

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  15. Find the differentiable function which satisfies the equation f(x)= -i...

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  16. Find all functions f(x) defined on (-pi/2,pi/2) with real values and h...

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  17. A tank contains 100 litres of fresh water. A solution containing 1 gm/...

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  18. A tank with a capacity of 1000 litres originally contains 100 gms of s...

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  19. (dy)/(dx)=y+int0^1 ydx given y=1 where x=0

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  20. Find the continuous function which satisfies the relation, int0^x t f(...

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