Q

# 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

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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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