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 October 3, 2011 Summary: 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 a 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) Modification rule If the form chosen for y p appears in y h , multiply your choice for y p by t , and recheck . (See Example 2 for an example of this).....
View
Full
Document
This note was uploaded on 02/03/2012 for the course M 427K taught by Professor Fonken during the Fall '08 term at University of Texas at Austin.
 Fall '08
 Fonken
 Differential Equations, Equations

Click to edit the document details