undetermined_steps - GE 207K Method of Undetermined...

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 Method of Undetermined Coefficients September 29, 2010 This page aims to recap our mini-lecture on solving 2nd order nonhomogeneous ODEs with constant coefficients using the method of undetermined coefficients. We are dealing with 2nd-order linear nonhomogeneous ordinary differential equations with constant coefficients which can be written as y 00 + ay + by = f ( t ) , (1) where a and b are two CONSTANTS , and f ( t ) is either a sine, cosine, exponential, or polynomial (or constant). In this method, we will wisely choose a form for the particular solution which will have some unknown coefficients. Later solve for these coefficients. Steps : 1. Find the corresponding homogenous solution, y h : Set the f ( t ) equal to zero, and find the corrensponding solution to the differential equation. In other words, solve the differential equation y 00 + ay + by = 0 (2) and call the solution y h . 2. Find the particular solution, y p : (i) For a given f ( t ) , choose a form for y p from table below: f ( t ) y p Ke t Ae t K cos t A cos t + B sin t K sin t Ke t cos t e t ( A cos t + B sin t ) Ke t sin t Kt 4 At 4 + Bt 3 + Ct 2 + Dt + E 1 , 5 , 10 , 31 , 59 , etc. A Kt 3 e t ( At 3 + Bt 2 + Ct + D ) e t (ii)...
View Full Document

Page1 / 5

undetermined_steps - GE 207K Method of Undetermined...

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