Math Questions

[TevashSzat]

Well, I'm expecting to have a great deal of math questions in the future because of a course I'm taking, so I guess I'm creating this thread for asking about some questions (mostly differential equations stuff) and for anyone else who might need to

Okay, first:

Given

R(dQ/dt) + Q/C = V

R: resistance
C: capacitance:
V: voltage
Q: charge

find Q(t) [treat R/C/V as constants]

Attempt/thoughts: (k is constant for after integration)

R(dQ/dt) = V-Q/C
RC(dQ/dt) = CV-Q
(dQ/dt)/(CV-Q) = 1/(RC)
ln(CV-Q) = t/(RC) + k
CV - Q = ke^(t/RC)
Q(t) = CV-ke^(t/RC)

Q(0)=0 [this is provided in prob] so
k = CV so

Q(t) = CV-CVe^(t/RC)

correct answer provided:

Q(t) = CV-CVe^(-t/RC)

So....kinda similar to what I got. So can anyone see what I did wrong? What I did seems pretty elementary and I can't find any problems with it