Hello PF! We were doing mass balances on mixing tanks in one of my ChemE courses, and in one of the problems we arrived at the following DE:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{dC_B}{d \theta} + 0.025C_B=0.0125 e^{-0.025 \theta}[/tex]

Where C_{B}is the concetration of salt in the tank and θ is time. The professor made us solve the equation using two methods, integrating factor and Laplace transform, and told us to keep working on following problems with the method of our choice. Personally, I preferred using the integrating factor method, because it is a very simple equation, and I don't like to be dealing with transform charts while solving problems, although I know that for more complex DEs the integrating factor method becomes really complicated, and Laplace transform remains relatively simpler. I think I'll be using integrating factor for simple equations like this, and LT for more complex differential equations, although I'm more inclined to use the integrating factor method. Also, which method do you think looks more elegant? Even though I'm an engineering student I always try to be "mathematically elegant," whenever it is possible. By the way, the solution of the equation is:

[tex]C_B= (0.0125 \theta +0.25) e^{-0.025 \theta}[/tex]

So, long story short, integrating factor or Laplace transform? Why? Which method do you think is more elegant?

Thanks in advance for any input!

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# Integrating factor vs. Laplace. Engineering problems

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