Section 3.9

# Section 3.9 - Notes for Day Â Variation of Parameters e...

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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Notes for Day : Â§ . : Variation of Parameters e Method of Variation of Parameters allows us to solve non-homogeneous second-order linear di erential equations of the form y â€²â€² + p ( t ) y â€² + q ( t ) y = g ( t ) when g ( t ) is not in the right form to allow us to solve using the Method of Undetermined Coe cients. Both methods accomplish the same goal. Variation of Parameters is more versati e, but genera y onger, than Undetermined Coe cients. e basic idea Suppose we have already solved the homogeneous di erential equation: y â€²â€² + p ( t ) y â€² + q ( t ) y = . Remember that we call this solution the complementary solution and use y C to represent it. e complementary solution takes the form: y C ( t ) = c y ( t ) + c y ( t ) , where c and c are constants. If instead, we allow functions u ( t ) and u ( t ) to be used in place of the constants, we get a particular solution instead: y P ( t ) = u ( t ) y ( t ) + u ( t ) y ( t ) , as long as the resulting function y P ( t ) solves the di erential equation.solves the di erential equation....
View Full Document

## This note was uploaded on 04/05/2008 for the course MATH 2214 taught by Professor Edesturler during the Spring '06 term at Virginia Tech.

### Page1 / 3

Section 3.9 - Notes for Day Â Variation of Parameters e...

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

View Full Document
Ask a homework question - tutors are online