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Unformatted text preview: Math 201 Fall 2011 Tutorial 6 Tuesday October 18 TAs: Points need to emphasize • Order of polynomial • If the guessed solution is a solution of the homogeneous equation, multiply it by x • what to do if g ( x ) is a product of polynomials, sin and cos , and e ax • what to do if g ( x ) is a product of polynomials, sin and cos , and e ax 1. Solve y 00 2 y = 4 x + 2 . • The general solution y g to y 00 2 y = 0 , – the auxiliary equation is λ 2 2 λ = 0 , λ 1 = 0 , λ 2 = 2 – y 1 = e λ 1 t = e x = 1 , y 2 = e λ 2 t = e 2 x – So, y g = c 1 y 1 + c 2 y 2 = c 1 + c 2 e 2 x . • A particular solution y p : – because the right hand side is a polynomial, we guess for a polynomial solution y p with order n . Note that the left hand side has an order n 1 , the right hans side has an order 1 , so n 1 = 1 , n = 2 , that is, we guess for a quadratic solution, y p = ax 2 + bx + c , – y 00 p 2 y 00 p = 2 a 2(2 ax + b ) = 4 ax + 2 a 2 b = 4 x + 2 – compare the coefficients of the polynomials on both sides,...
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This note was uploaded on 01/15/2012 for the course MATH 201 taught by Professor Steacy during the Winter '10 term at University of Victoria.
 Winter '10
 STEACY
 Polynomials

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