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I want to solve the Yb:YAG laser rate equations. I have three differential equation:

http://8pic.ir/images/61nyu3ya2dw5i0xc9iis_thumb.jpg

and the boundary conditions are:

http://8pic.ir/images/wa8ss3kjesg0vllnv7ju_thumb.jpg

the schematically figure of Yb:YAG crystal is:

http://8pic.ir/images/8igigmgmhr3lvqnj2edr_thumb.jpg

But in the above equations, I am confident the N1 and N0 parameters are changing but I can't recognize how they changed?is there an equation?

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# I have a problem in solving laser rate equation, I need help

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