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The equation of family of a curve is y^(...

The equation of family of a curve is `y^(2)=4a(x+a),` then differential equation of the family is

A

`x=y'+x`

B

`y=y"+x`

C

`y=2y'+y y^('2)`

D

`y"+y'+y^(2)=0`

Text Solution

Verified by Experts

The correct Answer is:
C
Given, `y^(2)=4ax+4a^(2)`
`implies2y y'=4a`
On putting the value of 4 a in Eq. (i)
we get
`y^(2)=2y y'x+4*(y^(2)y^('2))/(4)`
`impliesy=2y'x+y y^('2)`
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