1 Answer

Imkingdavid · Answer 1 · 2024-08-30T16:59:34+0000

The differential representing representing family of curves is
$(d^2y)/(dx^2) + a \sin(x + b) = 0$

The given family of curves is y=asin(x+b), where a and b are arbitrary constants.

To find the differential equation representing this family of curves, we need to express it in terms of the derivatives with respect to x.

First, let's find the first derivative of y with respect to x:

dy/dx=acos(x+b)

Now, let's find the second derivative:

$(d^2y)/(dx^2) =- a \sin(x + b)$

The differential equation representing the family of curves is then:

$(d^2y)/(dx^2) + a \sin(x + b) = 0$

Hence, the differential representing representing family of curves is
$(d^2y)/(dx^2) + a \sin(x + b) = 0$

Complete question:

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

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