Question

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

`y sqrt(1 + x^2) : y' = (xy)/(1+x^2)`

Answer 1

We have, `y = sqrt(1 + x^2)`             ....(1)

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

`y' = (1 xx (2x))/(2 sqrt (1 + x^2))`

⇒ `y' = x/ (sqrt(1 + x^2))`             ...(2)

Dividing (2) by (1), we get

`(y')/y = x/ (1 + x^2)`

⇒ `y' = (xy)/ (1 +x^2)`

Hence, `y = sqrt(1 + x^2)` is a solution of the given differential equation.