constant_coeff - GE 207K 2nd Order ODEs with Constant...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ....
View Full Document

Page1 / 4

constant_coeff - GE 207K 2nd Order ODEs with Constant...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online