Struggling with AP Multiple Choice: ky Differential Equation

AI Thread Summary
The discussion revolves around solving the differential equation dy/dt = ky, where k is a nonzero constant. Two suggested methods for tackling the AP multiple-choice problem include substituting each answer choice into the equation or using separation of variables and integration. The integration approach leads to the general solution y = Ae^(kt). Additionally, one participant suggests that differentiating each answer choice could also help identify the correct solution. The conversation emphasizes the importance of understanding differential equations in the context of AP exam preparation.
tandoorichicken
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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?
 
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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
 
Actually, for this problem, I suspect that most people would just differentiate each of the answers.
 
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