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racodelitusmn 2022-07-03 Answered
Solve the following system of differential equations
x ˙ = 2000 3 x y 2 x y ˙ = 3 x y 6 y z ˙ = 4 y 2 z
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Answers (2)

Zichetti4b
Answered 2022-07-04 Author has 13 answers
The solutions with x and y constant are x = 1000 , y = 0 , z = C e 2 t and x = 2 , y = 998 / 3 , z = 1996 / 3 + C e 2 t . You won't find closed-form solutions other than those, but you can get qualitative information from a phase-plane analysis in the x , y variables.

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Jovany Clayton
Answered 2022-07-05 Author has 4 answers
x ( t ) = 4 ( k + 1 ) 3 k y ( t ) = 2 ( 749 k 1 ) 3 ( k + 1 ) z ( t ) = e 2 t + 4 ( 749 k 1 ) 3 ( k + 1 )
where k is a constant
First solve z ˙ = 4 y 2 z

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