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Unformatted text preview: GE 207K 2nd Order ODEs with Constant Coeffs September 20, 2010 This page aims to recap our mini-lecture on solving 2nd order ODEs with constant coeffi- cients. We are dealing with 2nd-order 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