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A normal is drawn at a point `P(x , y)` of a curve. It meets the x-axis at `Qdot` If `P Q` has constant length `k ,` then show that the differential equation describing such curves is `y(dy)/(dx)=+-sqrt(k^2-y^2)` . Find the equation of such a curve passing through `(0, k)dot`

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CENGAGE PUBLICATION-DIFFERENTIAL EQUATIONS-All Questions
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  2. The general solution of the equation (dy)/(dx)=1+x y is

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

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  4. If the solution of the differential equation (dy)/(dx)-y=1-e^(-x) and...

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

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  6. If the dependent variable y is changed to z by the substitution ...

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  7. If the independent variable x is changed to y , then the differe...

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  8. If the solution of the differential equation (dy)/(dx)=1/(xcosy+sin2y)...

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  9. Tangent is drawn at the point (xi ,yi) on the curve y=f(x), which ...

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  10. If the eccentricity of the curve for which tangent at point P inter...

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

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  12. Find the order and degree of the following differential equations. i) ...

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  13. Form the differential equation of family of lines concurrent at the ...

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  14. Form the differential equation of all circle touching the x-axis at...

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  15. Form the differential equation of family of lines situated at a con...

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  16. From the differential equation of the family of parabolas with focus a...

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  17. The differential equation of all parabolas whose axis are parallel t...

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  18. Form the differential equation of the family curves having equation y=...

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  19. What is the order of the differential equation whose general solution ...

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  20. Find the particular solution of the differential equation (1+e^(2x))dy...

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