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MIT OpenCourseWarehttp://ocw.mit.edu 18.034 Honors Differential Equations Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.18.034 Recitation: April 2nd, 2009 1. Find the rest solution to the ODE y� + 2y = e 3t . 2. (a) Suppose |f(t)| ≤ C|eat| for some a > 0. Show that if F (s) = Q(s)/P (s) for polynomials P and Q, then deg P > deg Q. (b) Show that if |f�(t)| ≤ Ceat then lims→∞ sF (s) = f (0). 3. Find the Laplace transforms of (a) f(t) = cosh t sin t, (b) � t sin θ g(t) = dθ, θ0 2(c) h(t) = e−t(in as explicit a form as you can). 4. Find the inverse transform of 2s3 + 6s2 + 21s + 52 F (s) = . s(s + 2)(s2 + 4s + 13)


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MIT 18 034 - LECTURE NOTES

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