This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: GE 207K Method of Undetermined Coefficients September 29, 2010 This page aims to recap our minilecture on solving 2nd order nonhomogeneous ODEs with constant coefficients using the method of undetermined coefficients. We are dealing with 2ndorder 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
 Fall '10
 None

Click to edit the document details