Question

Find x(t) please i'm strugling; dx/dt = C + kx where c and x are constants? How do you get this x(t) = C/k (1 - exp(-kt)). I can't follow what happend please??

Answer 1

\[
\frac {dx}{C + k x}=dt \\
\int \frac {dx}{C + k x}=\int dt \\
\frac 1 k \ln(C+ k x)= t
\]

Answer 2

\[
x(t)=B e^{k t}-\frac{C}{k}
\]