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clynne21
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Homework Statement
Given the followin[Sg decay chain- X→Y→Z
Solve for Nx(t), Ny(t), Nz(t) for the case of Rx(t)=[itex]\alpha[/itex]t and assuming Ny(t)=Nz(t)=0
Homework Equations
dNx(t)/dt = -[itex]\lambda[/itex]xNx(t) + Rx(t)
dNy(t)/dt = -[itex]\lambda[/itex]yNy(t) +[itex]\lambda[/itex]xNx(t)
dNz(t)/dt = -[itex]\lambda[/itex]zNz(t) +[itex]\lambda[/itex]yNy(t)
The Attempt at a Solution
I know these would be solved with bateman equations and without the Rx(t)=[itex]\alpha[/itex]t term I could do these. The production term throws me off and I'm not sure exactly how to go about this.
I have this for Nx(t) = Nx(0)e-[itex]\lambda[/itex]xt + ∫t0 dt'Rx(t')e[itex]\lambda[/itex]x(t'-t) (the integral is from 0 to t, but the itex wasn't working for me to do that)
So how does Rx(t)=[itex]\alpha[/itex]t integrate and where does it go in the other two equations? Thanks!
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