What is the complete derivation of the nonhomogeneous fluid flow rate equation?

[fahadismath]

does anyone know the derivation of the general solution of the nonhomogeneous equation shown in the image (book name: Devendra K. Chaturvedi - Modeling and Simulation of Systems Using MATLAB and Simulink -CRC Press (2010))

 

[pasmith]

This is basic calculus.
$$\begin{split} \frac{dC}{dt} &= \frac{F}{V}(C_0 - C) \\ \int \frac{1}{C_0 - C}\frac{dC}{dt} \,dt &= \int \frac{F}{V}\,dt \\ \int \frac1{C-C_0}\,dC &= \ln |k| - \frac{F}{V}t \\ \ln |C - C_0| &= \\ C(t) &= C_0 + ke^{-Ft/V}.\end{split}$$ (We can drop the absolute value signs since $C - C_0$ and $k$ must have the same sign.)

 

[fahadismath]

in your derivation you didn't complete this step ln|C-Co|= ? KINDLY write the complete equation

 

[renormalize]

in your derivation you didn't complete this step ln|C-Co|= ? KINDLY write the complete equation

It equals the same as the right side of the line above it: $\ln |k| - \frac{F}{V}t$.