Question

Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:

y = Ax : xy′ = y (x ≠ 0)

Answer 1

We have, y = Ax                 ...(1)

Differentiating (1) w.r.t.x, we get,

y' = A                         ...(2)

Dividing (2) by (1), we get

`(y')/y = 1/x`

⇒ xy' = y

Hence, y = Ax is a solution of the given differential equation.