The order and the degree of the differential equation of all ellipses with centre at the origin,major axis along x-axis and eccentricity  \frac{\sqrt{3}}{2}  are, respectively :

  • Option 1)

    2,  2

  • Option 2)

    1,  1

  • Option 3)

    2,  1

  • Option 4)

    1,  2

 

Answers (1)

As we learnt in

Order of a Differential Equation -

The order of a differential equation is order of highest order occuring in differential equation

- wherein

order of

\frac{d^{2}y} {dx^{2}}+5=0  

is 2.

 

 

  Let the equation of ellipses is  \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1  and 1-\frac{b^{2}}{a^{2}}=\frac{3}{4}

\\ \therefore \frac{b^{2}}{a^{2}}=\frac{1}{4}\, \, \, \, \, \therefore a^{2}=4b^{2}

\\ \Rightarrow \frac{x^{2}}{4b^{2}}+\frac{y^{2}}{b^{2}}=1

\\ \Rightarrow x^{2}+{4y^{2}}=4b^{2}

\\ \Rightarrow 2x+{8y.\frac{dy}{dx}}=0

\therefore x+4y.\frac{dy}{dx}=0

Order (O) \rightarrow 1

Degree (D) \rightarrow 1


Option 1)

2,  2

This option is incorrect.

Option 2)

1,  1

This option is correct.

Option 3)

2,  1

This option is incorrect.

Option 4)

1,  2

This option is incorrect.

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