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you have dC/ (r - kC) = dt , correct?

let u = -kC , du = -k dC, so we have integral 1/u * du/-k = integral t

-1/k int u / du = int t

-1/k ln u = t + c

ln u = -kt + c1 , c1 is just a constant, not the concentration

so u = Ae^(-kt)

r - kC = Ae^(-kt)

kC -r = -Ae^(-kt) by multipling both sides by -1

C = r/k + A/k e^(-kt) , notice that it should be -A , but since its a constant it doesnt matter

i think i made a mistake

ok back to this step -1/k ln u = t + c

ln u = -k t + -k C oh nevermind

shadow i tried to take derivative of C = r/k + A/k e^(-kt)

C = [r- A e^(-kt) ] / k This is final general solution

now you need an initial condition

yeah i figured

[\int x]

[\x=2\]