Differential EquationHard

Question

The solution of (x + y + 1) dy = dx are

Options

A.x + y + 2 = Cey
B.x + y + 4= = C log y
C.log (x + y + 2) = Cy
D.log (x + y + 2) = C + y

Solution

= x + y + 1
⇒ - x - y - 1 = 0        I.F. = e-∫dy = e-y
⇒ e-y - xe-y - ye-y - e-y = 0
⇒ ∫d(Xe-y) = ∫(e-y + ye-y)dy
⇒ xe-y = - e-y - ye-y + ∫e-y dy
⇒  xe-y = -e-y - ye-y - e-y + c
⇒ x = - 1 - y - 1 + cey
⇒ x + y + 2 = cey

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