`y = x sin x : xy' = y + x sqrt(x^(2) - y^(2))(x ne 0 and x gt y or x lt -y)`

x dy - y dx = sqrt(x^(2) + y^(2)) dx

y = Ax : xy' = y (x ne 0)

y = sqrt(a^(2) - x^(2)) x ne (-a, a) : x + y (dy)/(dx) = 0(y ne 0)

2x-y gt 1, x-2y lt -1

x^(2)dy+(xy + y^(2))dx = 0, y = 1 when x = 1

2xy + y^(2) - 2x^(2)(dy)/(dx) = 0, y = 2 when x = 1

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

x+y ge 4, 2x-y lt 0

Verify (i) x ^(3) + y ^(3) = (x + y) (x ^(2) -xy + y ^(2)) (ii) x ^(3) -y ^(3) = (x-y) (x ^(2) +xy +y ^(2)) using some non-zone positive integers and check by actual multiplication. Can you call these as identities ?