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crosssbow

  • 2 years ago

create a 3 by3 system of ODE IVP from this problem: Suppose three chemical species are in a process of reaction, where every minute 20% of chemical A becomes chemical B, and 25% of chemical B become chemical C. There is no supply of chemical A. The reaction stops at chemical C. At present, there are 100 grams of chemical A, 20 grams of chemical B, and no chemical C. We are interested in the First 10 minutes of the reaction.

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  1. UnkleRhaukus
    • 2 years ago
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    so we need to find three equations

  2. crosssbow
    • 2 years ago
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    yes, i said x , y, and z

  3. crosssbow
    • 2 years ago
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    x=chem A y=chem B z=chem C

  4. crosssbow
    • 2 years ago
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    dx/dt=?? dy/dt=??? dz/dt=??

  5. crosssbow
    • 2 years ago
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    and i believe i know the interval [0,10]

  6. crosssbow
    • 2 years ago
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    since we are intrested in the first 10 min

  7. UnkleRhaukus
    • 2 years ago
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    so \[\frac{\text dA}{\text dt}=80\%A\]

  8. crosssbow
    • 2 years ago
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    why?

  9. UnkleRhaukus
    • 2 years ago
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    every minute 20% of chemical A becomes chemical B so every minute chemical A becomes 80% of was before

  10. crosssbow
    • 2 years ago
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    okay, that makes sense, how about for dB/dt?

  11. UnkleRhaukus
    • 2 years ago
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    every minute 20% of chemical A becomes chemical B, and 25% of chemical B become chemical C

  12. crosssbow
    • 2 years ago
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    20%A-25%B

  13. UnkleRhaukus
    • 2 years ago
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    and the last one/

  14. crosssbow
    • 2 years ago
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    i am not sure , maybe just 25%B??

  15. crosssbow
    • 2 years ago
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    ?

  16. UnkleRhaukus
    • 2 years ago
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    i think thats right

  17. crosssbow
    • 2 years ago
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    okay thanks

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