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

D.y=?A+Cekt

E.y=A?1+Ce?Akt

F.y=A+Ce?kt

Solution

dy/dt=k(Ay+1) dy/(AY+1)= k dt (1/A)ln(Ay+1)=kt +c Ay+1=e^(Akt) +C y=(1/A)e^(Akt) + C\' A is the correct answer