lecture16 - Section 6.3 Annihilator Method March 25, 2009...

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Unformatted text preview: Section 6.3 Annihilator Method March 25, 2009 Annihilator Method Todays Session Exam 2 is April 2 (Next Thursday) It covers 4.1-4.5, 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 contd To find a particular solution for ay + by + cy = P m ( t ) e t cos t + Q m ( t ) e t sin 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 t cos t + t s parenleftBig B + B 1 t + . . . + B k t k parenrightBig e t sin t . Here k = max( m , n ), s = 0 if + i is not a root of the characteristic equation; and s = 1 if + i is a root of the characteristic equation....
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lecture16 - Section 6.3 Annihilator Method March 25, 2009...

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