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Help me solve this - Differential equations - JEE Main-3

The degree and order of the differential equation of the family of all parabolas whose axis is x-axis, are respectively

  • Option 1)

    1, 2

  • Option 2)

    3, 2

  • Option 3)

    2, 3

  • Option 4)

    2, 1

 
Answers (1)
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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

-

 

  Let the equation of Parabola be:

y^{2}=4a(x-b)

2yy'=4a

\therefore y=2y'(x-b)

\Rightarrow y'=2y'+2y''\:(x-b)

\Rightarrow -y'=2y''\:.\:\frac{y}{2y'}=\frac{yy''}{y'}

\Rightarrow yy''+(y')^{2}=0

Order is 2

Degree is 1

 


Option 1)

1, 2

This option is correct.

Option 2)

3, 2

This option is incorrect.

Option 3)

2, 3

This option is incorrect.

Option 4)

2, 1

This option is incorrect.

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