The differential equation for the family of curves x^{2}+y^{2}-2ay=0, where a is an arbitrary constant is

  • Option 1)

    (x^{2}-y^{2})y'=2xy

  • Option 2)

    2(x^{2}+y^{2})y'=xy

  • Option 3)

    2(x^{2}-y^{2})y'=xy

  • Option 4)

    (x^{2}+y^{2})y'=2xy

 

Answers (1)

As we learnt in 

Formation of Differential Equations -

A differential equation can be derived from its equation by the process of differentiation and other algebraical process of elimination

-

 

 x^{2}+y^{2}-2ay=0

2x+2y\frac{dy}{dx}-2a.\frac{dy}{dx}=0

\Rightarrow x+y\frac{dy}{dx}=a\frac{dy}{dx}

\Rightarrow x+y\frac{dy}{dx}=\frac{x^{2}+y^{2}}{2y}.\frac{dy}{dx}

2xy+2y^{2}\frac{dy}{dx}= x^{2}\frac{dy}{dx}+y^{2}\frac{dy}{dx}

(x^{2}-y^{2})\frac{dy}{dx}=2xy

 


Option 1)

(x^{2}-y^{2})y'=2xy

Correct option

Option 2)

2(x^{2}+y^{2})y'=xy

Incorrect option

Option 3)

2(x^{2}-y^{2})y'=xy

Incorrect option

Option 4)

(x^{2}+y^{2})y'=2xy

Incorrect option

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