My Math Forum  

Go Back   My Math Forum > College Math Forum > Differential Equations

Differential Equations Ordinary and Partial Differential Equations Math Forum

Thanks Tree1Thanks
  • 1 Post By SDK
LinkBack Thread Tools Display Modes
October 29th, 2017, 12:49 PM   #1
Joined: Oct 2017
From: venezuela

Posts: 3
Thanks: 0

This differential equation is driving me crazy...

Hello There, I am david, i am new in the forum and really hope you cold help me.

I am supose to solve this differential equations which is making me going crazy

[1] d(Ca)/d(t) = (-k*Ca*Cb) -(q*Ca/V)
[2] d(Cb)/d(t) = (-k*Ca*Cb) + (q*(Cbo-Cb)/V)
[3] d(Cc)/d{t) = (k*Ca*Cb) - (q*Cc/V)
[4] d(Cd)/d(t) = (k*Ca*Cb) - (q*Cd/V)

This equations are the result of a molar-mass balance in a semibatch reactor.

I am suppose to graphic reaction velocity (r) vs time (t)

There is some extra information

[1] k = 2.2
(2) q = 0.05
(3] Cbo",0.025
[4] Vo=5
(5] Cao = 0.05
[6] r = k*Ca*Cb
[7 J V = Vo + q*t
[8] X = (Cao*Vo-Ca*V)/(Cao·Vo)

In the book i got this from they solve the problem with polymath but my teacher want us to do it manually (a real pain the in ass) If somebody could tell me at least how i am suppose to resolve the first equation i would really apreciate, thanks for taking your time to read this and i apoligize if my grammar is not correct
davix5055 is offline  
October 29th, 2017, 04:59 PM   #2
Global Moderator
greg1313's Avatar
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,642
Thanks: 960

Math Focus: Elementary mathematics and beyond
Any ideas on how to begin?
greg1313 is offline  
October 29th, 2017, 05:49 PM   #3
Joined: Oct 2017
From: venezuela

Posts: 3
Thanks: 0

I tried a couple of things (variable separations, 1st order linear differential equation but kinda got stuck because Cb also depens on t) so I dont know if there is other way to solve it, maybe using a system of ecuations?
davix5055 is offline  
October 29th, 2017, 07:59 PM   #4
Math Team
topsquark's Avatar
Joined: May 2013
From: The Astral plane

Posts: 1,659
Thanks: 652

Math Focus: Wibbly wobbly timey-wimey stuff.
Are you sure you have the equations right? I'm getting a seriously ugly expression for Ca involving a number of Gamma and Bessel functions. (I'd show you the solution using Wolfram Alpha, but it doesn't know how to do it. I had to do it on my personal copy of Mathematica.)

Here's a quick rundown of what I did to get the equation for Ca:
1) Subtract equations 1 and 2 to remove the CaCb terms.

2) Set X = Ca - Cb.

3) Solve for X(t)

4) Find Cb = Ca - X

5) Put this into equation 1.

You get the equation $\displaystyle C_a'(t) = -k C_a^2 + k P e^{-qt/V} + k C_{b0} C_a$
Where P is an integration constant.


Last edited by topsquark; October 29th, 2017 at 08:05 PM.
topsquark is offline  
October 29th, 2017, 08:00 PM   #5
Senior Member
Joined: Sep 2016
From: USA

Posts: 197
Thanks: 105

Math Focus: Dynamical systems, analytic function theory, numerics
It is already a system of equations with 4 variables. As it is nonlinear and coupled I don't know what you mean by "solve by hand". The best you can hope for is to expand a solution in a power series since the RHS is analytic.
Thanks from topsquark
SDK is offline  
October 30th, 2017, 10:46 AM   #6
Joined: Oct 2017
From: venezuela

Posts: 3
Thanks: 0

My teacher said we could make this system of equations using laplace transform, i will give it a shot, Thanks for thanking your time for answering me, i really appreciate it
davix5055 is offline  

  My Math Forum > College Math Forum > Differential Equations

chemistry, crazy, differential, driving, equation

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
u substitution driving me crazy dthiaw Calculus 1 May 23rd, 2017 04:59 PM
I have this homework that is driving me crazy DANDIS Advanced Statistics 2 December 24th, 2011 02:12 PM
An easy equation driving me crazy failiure Algebra 9 August 7th, 2011 10:26 AM
Trigonomic Identity!! Driving me CRAZY wowbringer Algebra 3 January 28th, 2011 07:09 PM
THIS QUESTION IS DRIVING ME CRAZY.. PLZ HELP !! kzeidan Algebra 3 January 25th, 2009 01:33 PM

Copyright © 2017 My Math Forum. All rights reserved.