This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Section 6.3 Annihilator Method March 25, 2009 Annihilator Method Today’s Session Exam 2 is April 2 (Next Thursday) It covers 4.14.5, 6.3 A sample exam is now online For clicker points and disputes regarding them, please come to office hours next week and bring your clicker with you. I cannot deal with these issues by email. Bring your clickers on Tuesday for the Review Session for Exam 2. A Summary of This Session: (1) General Rules for finding particular solution involving sin and cos. (2) Annihilator Method, by Example. Annihilator Method Method of Undertermined Coefficients (rule p. 200) To find a particular solution for ay ′′ + by ′ + cy = P m ( t ) e r t where P m ( t ) is a polynomial of degree m , use the form y p = t s ( A + A 1 t + . . . + A m t m ) e r t where s = 0 if r is not a root of the characteristic equation; s = 1 if r is a simple root of the characteristic equation; and s = 2 if r is a double a root of the characteristic equation. Annihilator Method Rule p. 200 cont’d To find a particular solution for ay ′′ + by ′ + cy = P m ( t ) e α t cos β t + Q m ( t ) e α t sin β t where P m ( t ) and Q n ( t ) are polynomials of degrees m and n , use the form y p = t s parenleftBig A + A 1 t + . . . + A k t k parenrightBig e α t cos β t + t s parenleftBig B + B 1 t + . . . + B k t k parenrightBig e α t sin β t . Here k = max( m , n ), s = 0 if α + i β is not a root of the characteristic equation; and s = 1 if α + i β is a root of the characteristic equation....
View
Full Document
 Spring '09
 Lotfi
 Differential Equations, Equations, Characteristic polynomial, Complex number, 5T, Annihilator method

Click to edit the document details