firstord_undet - UNDETERMINED COEFFICIENTS for FIRST ORDER...

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: UNDETERMINED COEFFICIENTS for FIRST ORDER LINEAR EQUATIONS This method is useful for solving non-homogeneous linear equations written in the form dy dx + k y = g ( x ) , where k is a non-zero constant and g is 1. a polynomial, 2. an exponential e rt , 3. a product of an exponential and a polynomial, 4. a sum of trigonometric functions sin ( t ), cos ( t ), 5. a sum of products e rt sin ( t ) , e rt cos ( t ), 6. a sum of terms p ( t ) , sin ( t ) + q ( t ) cos ( t ), where p and q are polynomials. Here are a couple more examples. Example 1: Find the general solution of y- 4 y = 8 x 2 . Here we take a trial solution to be a general polynomial of degree two y p ( x ) = A x 2 + B x + C . Then y p ( x ) = 2 Ax + B and substituting we have (2 A x + B )- 4 ( A x 2 + B x + C ) = 8 x 2 . Now, collecting like powers of x we rewrite this equation as- 4 A x 2 + (2 A- 4 B ) x + ( B- 4 C ) = 8 x 2 , and comparing coefficients of like terms on both sides of the equation gives- 4 A =...
View Full Document

This note was uploaded on 12/02/2009 for the course MATH 352 taught by Professor Staff during the Spring '08 term at University of Delaware.

Page1 / 2

firstord_undet - UNDETERMINED COEFFICIENTS for FIRST ORDER...

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