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Solve an ordinary differential equation

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Solve an ordinary differential equation in the attached file.

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https://brainmass.com/math/ordinary-differential-equations/solve-ordinary-differential-equation-88420

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Solution:
This is a linear Ordinary Differential Equation (ODE):
The theory section is given at the reference.
Write down the characteristic equation
r2 - 3r - 4 = 0
The solution to this problem is
r = -1 OR r = 4
Since these are two distinct real numbers, the ...

Solution Summary

The solution provides explanations on the theory of ordinary differential equation and then step-by-step instructions to solve the problem.

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Solving two independent ordinary differential equations

Two tanks A and B, each of volume V, are filled with water at time t=0. For t > 0, volume v of solution containing mass m of solute flows into tank A per second; mixture flows from tank A to tank B at the same rate and mixture flows away from tank B at the same rate. The differential equations used to model this system are given by:

d(SA)/dt+v/V*SA= m/V
&
d(SB)/dt+v/V*SB= v/V*SA

Where S stands for sigma (concentration of solute) in tank A or B.

Show that the mass of solute in tank B is given by:

mV/v *{1-e^(-vt/V)} - mt*e^(-vt/V)

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