∇・D = ρ
∇・B = 0
∇×E = - ∂B/∂ｔ
∇×H = i + ∂D/∂ｔ
taking divergence of the last equation,
∇・（∇×H ) = 0 = ∇・( i + ∂D/∂ｔ) = ∇・i + ∂(∇・D)/∂ｔ) = ∇・i + ∂ρ/∂ｔ
∇・i + ∂ρ/∂ｔ = 0 (charge conservation)
by way of trial, taking divergence of the third equation,
∇・(∇×E) = - ∂∇・B/∂ｔ
the left is zero using a formula of vector analysis,
the right also zero because ∇・B = 0, the second equation.
the results are trivial.