Let A and k be positive constants Which of the given functio

Let A and k be positive constants. Which of the given functions is a solution to dy/dt = k(1 - Ay)? y = A^-1 +Ce^Akt y = -A + Ce^-kt y = A^-1 + Ce^-Akt y = -A + Ce^kt y = A + Ce^kt

Solution

Easy way to solve the problem:

Differentiate each of the answer. Check which of the differentials gives k(1-Ay)

Take A,

Differentiating option A:

dy/dt = C(Ak)e^Akt = (AkC)e^kAt

and, putting value of A in k(1 - Ay)

= k(1-A*(A^-1 -Ce^Akt)) = k (1 -1+ACe^Akt)

= (ACk)e^Akt

Both are equal. Hence , A is the right option