Question

Show that y2+ x-3 =0 is an implicit solution to dy/dx =-1/ (2y) on the interval (- [infinity] , 3)

Answer 1

Implicit function

`(d y)/(d x) = (-1)/(2y)`

Explanation:

Explanation:-

Given y² + x - 3=0 ...(i)

Differentiating equation (i) with respective to 'x', we get

`2 y (d y)/(d x) +1 = 0`

⇒
`2 y (d y)/(d x) = -1`

⇒
`(d y)/(d x) = (-1)/(2y)`

`(d y)/(d x) = (-1)/(2 (3))`

`(d y)/(d x) = (-1)/(6)`