Find the differential equation representing the family of curves y=asin (x+b), where a,b are arbitrary constants.

Explanation

we have `y^2 =a(ax+b)`

⇒`y^2 =a^2 x+ab`

On differentiating w.r.t x we get

`2y dy/dx =a^2`

⇒`y dy/dx = a^2/2`

⇒`y d^2y/dx^2+ dy/dx . dy/dx =0`

`y.y^2+(y^1)^2 =0`

Hence order and degree of the given equation is 2 and 1, respectively