Struggling with AP Multiple Choice: ky Differential Equation

[tandoorichicken]

Heres an AP multiple choice problem that's giving me some trouble:

If $$\frac{\,dy}{\,dt} = ky$$ and k is a nonzero constant, then y could be

a) $2e^{kty}$
b) $2e^{kt}$
c) $e^{kt} +3$
d) $kty + 5$
e) $\frac{1}{2}ky^2 + \frac{1}{2}$

Dont quite know where to begin?

 

[cookiemonster]

You have two choices.

#1 (probably the hardest way, but useful if you forgot how to solve it): Take all of the answers and plug them in. See which one works.

#2: Separate the variables and integrate.

dy/y = k*dt
ln(y) = kt + C
y = e^(kt + c) = Ae^(kt)

cookiemonster

 

[HallsofIvy]

Actually, for this problem, I suspect that most people would just differentiate each of the answers.