Assignment4 - A decays to B with decay constant k 1 , and B...

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Assignment #4 Due: At the START of tutorial on June 29, 2011. No late assignments will be accepted. 1. Consider the diFerential equation y ± ± ± + 5 y ± ± + 8 y ± + 6 y = x . Given that e x cos x is a solution to the homogeneous version of the equation, find the general solution. 2. Give the diFerential equation which has the following solution. ±or each, you must show your work in order to receive any credit. (a) y = c 1 + c 2 e - x + c 3 e 2 x - xe - x (b) y = x [ c 1 cos(2 ln x ) + c 2 sin(2 lnx )] + ln x + 3 3. Solve the following diFerential equations (a) t 2 y ± ± - 2 y = t 2 ln t (b) y ± ± - 2 y ± + 2 y = e x tan x (c) x 2 y ± ± - xy ± + y = x 2 (d) x 3 d 3 y dx 3 + 5 x 2 d 2 y dx 2 + 7 x dy dx + 8 y = 0 (e) y ± ± - 1 x y ± = - ( y ± ) 2 x 4. Consider a nuclear decay sequence in which nucleus
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Unformatted text preview: A decays to B with decay constant k 1 , and B further decays to nucleus C with decay constant k 2 : A → B and B → C (a) Describe this process as three first-order linear ODEs. (b) Show that by combining the two d.e. involving dA dt and dB dt we can obtain the 2nd order linear ODE in B alone: d 2 B dt 2 + ( k 1 + k 2 ) dB dt + k 1 k 2 B = 0 (c) If k 1 ± = k 2 , solve this diFerential equation by knowing the initial condition A (0) = A and B (0) = 0. 1...
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This note was uploaded on 01/15/2012 for the course MATH 201 taught by Professor Steacy during the Fall '10 term at University of Victoria.

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