Solve Calc Problem: Find y if dy/dt=ky and k is a Nonzero Constant

[radtad]

We have a set of problems for hw. I am stuck on 1 where I know the answer but can't seem to get it.

If dy/dt=ky and k is a nonzero constant then y could be
a. 2e^kty b. 2e^kt c. e^kt d. kty+5 e. 1/2ky^2 +1/2

I know the answer is b but i can't get that answer
Here is my work
S=integral sign

dy/dt=ky
dy/y=kdt
Sdy/y=kSdt
lny=kt
e^lny=e^kt
y=e^kt

How do u get a 2 in there for choice b

 

[jamesrc]

You forgot about the constant of integration:
\frac{dy}{dt}=ky
\frac{dy}y=kdt
\int{\frac{dy}y} = \int{kdt}
\ln y = kt +C
e^{\ln y} = e^{kt + C}
y = e^{kt}\cdot e^C
e^C is also a constant, so it can be written as C₁ if you like.The value of C₁ will depend on the initial conditions. Unless there's a typo in your answer list, I can see two answers that are of this form:
b. y=2e^{kt}
and c. y = e^{kt}

I hope that helps.

 

[radtad]

thanks forgot the C and yea choice c was a typo it should be e^kt +3