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5.1 - 5.1 Basic Definitions 1st Order Systems Governing...

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62 5.1 Basic Definitions 1st Order Systems Governing equations Governing equation is an ordinary differential eqn. (ODE) with only 1 st order derivatives Consider Linear Eqn.: () dx x Ft dt μ += μ = constant & positive t = independent variable, e.g. time General Solution 1 tt x eC e F t d t μμ =+ ⎩⎭ made up of 2 parts that are additive First part is solution for F ( t ) = 0 (homogenous) which is t x Ce = Note: this eqn. describes an
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