lecture14

lecture14 - Section 4.4, contd Method of Undetermined...

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Unformatted text preview: Section 4.4, contd Method of Undetermined Coefficients March 12, 2009 Method of Undetermined Coefficients Todays 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, contd...
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lecture14 - Section 4.4, contd Method of Undetermined...

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