LetAandkbe positive constants Which of the given functions i

LetAandkbe positive constants. Which of the given functions is a solution todtdy=k(Ay?1)

A.y=A?1+CeAkt

B.y=A+Cekt

C.y=?A+Ce?kt

E.y=A?1+Ce?Akt

F.y=A+Ce?kt

Solution

dy/dt= k(Ay+1) =>dy/(Ay+1) = kdt =>ln(Ay+1) = kAt + C =>Ay+1 = e^(kAt + C) hence option a is the answer