Working a problem in Greenburgs "Advanced Eng. Mathematics", #8 page 170. Two substances w/ concentration x(t) and y(t), react to form a 3rd substance w/ concentration z(t). The reaction is governed by the system(adsbygoogle = window.adsbygoogle || []).push({});

x’+ αx = 0

z’= βy

x + y + z = γ

solve for x(t), y(t), and Z(t) subject to intitial conditions

z(0)=z'(0)=0

for these cases: α≠β,α=β

My approach…I would like set the equation such that:

x’+ αx = 0

z’ – βy = 0

and set

L1= 1, L2=α,

L3= 1, L4= -β

(Where α≠β, α=β for the 2 cases) and use Cramer’s rule to solve…but I am missing the relationship between all three: x + y + z = γ

What I am missing? I have never done a problem with 3 variables. :yuck:

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# Chemical Reactions

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