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Show that the curve such that the distan...

Show that the curve such that the distance between the origin and the tangent at an arbitrary point is equal to the distance between the origin and the normal at the same point `sqrt(x^2+y^2) =ce^(+-tan^(-1y/x))`

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MOTION-DIFFERENTIAL EQUATION -Exercise 3
  1. Solve (x-y)dy=(x+y+1)dx

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  2. (dy)/(dx)=(x+y+1)/(2x+2y+3)

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  3. Show that the curve such that the distance between the origin and the ...

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  4. Let f(x, y, c1) = 0 and f(x, y, c2) = 0 define two integral curves of ...

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  5. Let y=y(t) be a solution to the differential equation y^(prime)+2t ...

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  6. Solution of the differential equation (1-x^(2))(dy)/(dx)+2xy=xsqrt(1-x...

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  7. Solve the following differential equation: (1+y^2)dx=(tan^(-1)y-x)dy

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  8. dy/dx -yln2 = 2^sinx. (cosx-1) ln 2, y being bounded when x rightarrow...

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  9. Consider the differential equation. Dy/dx +P(x)y = Q(x) (i) If two par...

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  10. x(1+y^2)dx-y(1+x^2)dy =0

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  11. Find the integral curve of the differential equation, x(1–x lny). Dy/d...

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  12. A tank consists of 50 litres of fresh water. Two litres of brine each ...

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  13. A normal is drawn at a point P(x , y) of a curve. It meets the x-ax...

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  14. Find the curve for which the sum of the lengths of the tangent and sub...

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

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

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

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

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

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

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