s11_mthsc208_hw02

s11_mthsc208_hw02 - MthSc 208, Spring 2011 (Differential...

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Unformatted text preview: MthSc 208, Spring 2011 (Differential Equations) Dr. Macauley HW 2 Due Wednesday January 26th, 2010 (1) Consider the initial value problem y = t + y, y(0) = 1. (a) When computing a solution by hand using Euler's method, it is beneficial to arrange your work in a table, as shown below where the first step is computed. Continue with Euler's method using step-size h = 0.1 and complete all missing entries of the table. k 0 1 2 3 4 5 tk 0.0 0.1 0.2 0.3 0.4 0.5 yk 1.0 1.1 f (tk , yk ) = tk + yk 1.0 h 0.1 f (tk , yk ) h 0.1 (2) (3) (4) (5) (6) (7) (b) The general solution of y = t + y is y(t) = Cet - t - 1. Using this, compute the actual value of y(0.5). Consider the initial value problem y = (1 + t)y, y(0) = -1. (a) Use Euler's method to approximate y(1), for step-size h = 0.2, and then for h = 0.1. Arrange your results in the tabular form as in the previous exercise. (b) Compute the actual value of y(1) by solving the initial value problem y = (1 + t)y, y(0) = -1 and plugging in t = 1. Solve for t, and simplify whenever possible. (a) 3e-4t = 5 (b) 2 = e3 e2t (c) t2 = e6 4 (d) ( 3 )-t = 7 1 (e) e 3 ln t = 27 1 (f) e- 3 ln t = 27 Compute the following integrals: 1 (a) 2t dt 1 (b) 3-4t dt Find the general solution of the following differential equations. (a) y = ty (b) ty = -2y (c) y = et-y Suppose that $1200 is invested at a rate of 5%, compounded continuously. (a) Assuming no additional withdrawals or deposits, how much will be in the account after 10 years? (b) How long will it take the balance to reach $5000? Tritium is an isotope of hydrogen that is sometimes used as a biochemical tracer. Suppose that 100 mg of tritium decays to 80 mg in 4 hours. Determine its half-life. ...
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This note was uploaded on 03/11/2012 for the course MTHSC 208 taught by Professor Staufeneger during the Spring '09 term at Clemson.

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