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4.4 Notes - y c Step 2 –"Guess" at a particular...

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Slide 1 Undetermined Coefficients Superposition Approach Differential Equations Section 4.4 Slide 2 When does this approach work? The coefficients on the left-hand side of the differential equation must be constants. g (x) must be either a constant, a polynomial function, an exponential function e ax , a sine or cosine function sin βx or cos βx , or finite sums and products of these functions. Slide 3 Method of Solution Step 1 Solve the associated homogeneous equation to obtain the complementary function
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Unformatted text preview: y c . Step 2 – "Guess" at a particular solution of the homogeneous equation and equate coefficients to obtain the particular solution y p . – Refer to Table 4.1 on p.172 if necessary until you get the hang of "guessing". Step 3 – Write the general solution y = y c + y p . Slide 4 What's the catch? If any terms in y p are duplicates of terms in y c , then you must multiply by x n , where n is the smallest positive integer that eliminates that duplication....
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4.4 Notes - y c Step 2 –"Guess" at a particular...

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