10-21-review

10-21-review - Friday Diﬀerential Equations — Fall 2011...

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Unformatted text preview: Friday, 10/21/11 Diﬀerential Equations — Fall 2011 In-class review for Section 7.6 1 Express the piecewise deﬁned function 2 0 f (t) = t5 sin t 0 < t < 3, 3 < t < 7, 7 < t < 9, t>9 in a single line in terms of Heaviside functions. 2 Find the Laplace transform of the solution y to the initial value problem 2y − 3y + y = 3 t2 0 < t < 5, sin t t > 5 y (0) = 1; Suppose that L {y } = e−2s + se−3s . s2 + 4 What is y ? One more problem on the back... y (0) = 0. Friday, 10/21/11 Diﬀerential Equations — Fall 2011 4 The half-rectiﬁed sine wave is equal to sin t when sin t is positive, and 0 otherwise. 1 π 2π 3π 4π 5π −1 Find the Laplace transform of the half-rectiﬁed sine wave. 6π ...
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10-21-review - Friday Diﬀerential Equations — Fall 2011...

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