Lecture 14

# Lecture 14 - Section 4.4 cont’d Method of Undetermined...

This preview shows pages 1–5. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

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: Section 4.4, cont’d Method of Undetermined Coefficients March 12, 2009 Method of Undetermined Coefficients Today’s Session A useful website: http://www.quickmath.com/ A Summary of This Session: (1) Method of undetermined coefficients, general rules (2) More examples Method of Undetermined Coefficients Method of Undertermined Coefficients (rule p. 193) When seeking a particular solution to the equation: a y ′′ + b y ′ + c y = C x n e rx we look for a solution of the form: y p = x s ( A + A 1 x + A 2 x 2 + . . . + A n x n ) e r x with: (i) s = 0 if r is not a root of the associated characteristic equation (ii) s = 1 if r is a simple root of the associated characteristic equation (iii) s = 2 if r is a double root. Method of Undetermined Coefficients Example 1 Determine the form of the particular solution, then find it. y ′′- 2 y ′ + 3 y = f ( t ) Make sure to find the form of y h first. (i) f ( t ) = t 2 e 2 t + e 5 t + t + 3 (ii) f ( t ) = 3 t 2 e − 3 t + e t (iii) f ( t ) = te t (iv) f ( t ) = e t + e − 3 t + e 2 t Method of Undetermined Coefficients Example 1, cont’d...
View Full Document

{[ snackBarMessage ]}

### Page1 / 12

Lecture 14 - Section 4.4 cont’d Method of Undetermined...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online