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Unformatted text preview: GE 207K 2nd Order ODEs with Constant Coeffs September 20, 2010 This page aims to recap our minilecture on solving 2nd order ODEs with constant coeffi cients. We are dealing with 2ndorder linear homogeneous ordinary differential equations with con stant coefficients (note all the characteristics associated pay special attention to the term constant coefficients), whose standard form is given by y 00 + Ay + By = 0 , (1) where A and B are two CONSTANTS . We solve these differential equations by saying that our solutions appear in the form of y = e rt , where r is a constant . By requiring that y = e rt be a solution, we end up with the corresponding characteristic equation for the ODE: r 2 + Ar + B = 0 . (2) Recall from algebra that Eq. ( 2 ) is a quadratic equation with three possible solution types: Real and distinct roots i.e. r 1 6 = r 2 . Real and repeated roots i.e. r 1 = r 2 ....
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 Fall '10
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