The general equation of the differential equation $\frac{dy}{dx}={{e}^{x+y}}is(A){{e}^{x}}+{{e}^{-y}}=c(B){{e}^{x}}+{{e}^{y}}=c(C){{e}^{-x}}+{{e}^{y}}=c(D){{e}^{-x}}+{{e}^{-y}}=c$