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 ellipse is 

\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\:\:\:but\ 1-\frac{b^{2}}{a^{2}}=\frac{3}{4}

\therefore \frac{x^{2}}{4b^{2}}+\frac{y^{2}}{b^{2}}=1\:\:\:\therefore \frac{b^{2}}{a^{2}}=\frac{1}{4}

\therefore x^{2}+4y^{2}=4b^{2}\:\:\:\therefore a^{2}=4b^{2}

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

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

order=1\\ degree=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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