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}<br /> \frac{dC}{dt} &amp;= \frac{F}{V}(C_0 - C) \\<br /> \int \frac{1}{C_0 - C}\frac{dC}{dt} \,dt &amp;= \int \frac{F}{V}\,dt \\<br /> \int \frac1{C-C_0}\,dC &amp;= \ln |k| - \frac{F}{V}t \\<br /> \ln |C - C_0| &amp;= \\<br /> C(t) &amp;= 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: $\ln |k| - \frac{F}{V}t$.