Please answer in the style of a formal proof and thoroughly reference any theorems, lemmas or corollaries utilized.

In the ODE included below I am wanting to prove the solution Always Exists and is Unique for all t>=0. The parameters (can be treated as constants) a,b,c,f>=0, 0<=d<1, where A_m is a constant >A for all t.

Below the equation I included the solution from WolframAlpha, where the parameters are changed slightly to work in Wolfram.

If additional assumptions for the parameters are needed or more information in general please let me know what would help!

 

Equation rewritten in WolframAlpha and the solution from that site.

Transcribed Image Text:

dA a + b|1 dt А f – dA Am · e-ct dA a + b|1 dt А f – dA Am · e-ct

Answer rating: 100% (QA)

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