Question

Solve the given differential equation dN/dt=kN, (k=constant)

Answer 1

\[\frac{dN}{dt}=kN \rightarrow dN \left( \frac{1}{N} \right)=k dt\]
\[\int\limits N^{-1}dN=k \int\limits dt \implies \ln|N|=kt+C\]
\[e^{\ln|N|}=e^{kt+c} \rightarrow N=e^{kt}{e^c}\]
Call e^c your new constant.
\[N=Ce^{kt}\]

Answer 2

Make sense scotty?

Answer 3

Yes, I got it to the end but didnt know I can make C=e^c. Thank you very much!

Answer 4

Yeah, if you had like +Ae^t+Be^t You can make that: e^t(A+B) then just call it Ce^t.