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10 cards from this deck
They show how a variable y changes based on itself.
Solutions where g(y_0) = 0, meaning y stays constant.
To isolate y and x for easier solving of equations.
Separate variables and integrate: y = Ce^(kt).
It provides ln|y| = kx + C after separation.
Use initial or boundary conditions to determine C.
Steady states are at y = 0 and y = -1 (not valid).
Logistic growth: dy/dx = ry(1-y/C).
Check if they satisfy the original equation and conditions.
They model growth, chemical reactions, and system behaviors.
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