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November 22nd, 2016, 10:12 AM  #11 
Global Moderator Joined: Dec 2006 Posts: 16,368 Thanks: 1172 
Using dx/dt + x  y = 1, dy/dt + 27x  9y = 6e^(4t)  9, with x = 3 and y = 18 when t = 0, the solution of this system is as shown below. x = (√2sin(√2t) + 3)e^(4t), y = (5√2sin(√2t) + 2cos(√2t) + 15)e^(4t) + 1 (with thanks to WolframAlpha). 

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