Struggling with AP Multiple Choice: ky Differential Equation

[tandoorichicken]

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

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

a) [itex] 2e^{kty}[/itex]
b) [itex] 2e^{kt}[/itex]
c) [itex] e^{kt} +3[/itex]
d) [itex] kty + 5 [/itex]
e) [itex] \frac{1}{2}ky^2 + \frac{1}{2}[/itex]

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.