## crosssbow 3 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.

1. UnkleRhaukus

so we need to find three equations

2. crosssbow

yes, i said x , y, and z

3. crosssbow

x=chem A y=chem B z=chem C

4. crosssbow

dx/dt=?? dy/dt=??? dz/dt=??

5. crosssbow

and i believe i know the interval [0,10]

6. crosssbow

since we are intrested in the first 10 min

7. UnkleRhaukus

so $\frac{\text dA}{\text dt}=80\%A$

8. crosssbow

why?

9. UnkleRhaukus

every minute 20% of chemical A becomes chemical B so every minute chemical A becomes 80% of was before

10. crosssbow

okay, that makes sense, how about for dB/dt?

11. UnkleRhaukus

every minute 20% of chemical A becomes chemical B, and 25% of chemical B become chemical C

12. crosssbow

20%A-25%B

13. UnkleRhaukus

and the last one/

14. crosssbow

i am not sure , maybe just 25%B??

15. crosssbow

?

16. UnkleRhaukus

i think thats right

17. crosssbow

okay thanks