grp_prj_extra - and show that the system is its own...

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Group project 1: MAC 2302 (Sec 0693) Due on 9th June,2011. Please write in detail your solution in a separate paper clearly.You also need to present the problem in class on the due date. Choose any one from the following list. Total Points: 30 1. Obtain the differential equation for the confocal conics, x 2 a 2 + λ + y 2 b 2 + λ = 1 where λ is a general constant,
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Unformatted text preview: and show that the system is its own orthogonal trajectory. 2. Show that (4 x + 3 y + 1) dx + (3 x + 2 y + 1) dy = 0 represents a family of hyperbolas having as asymptotes the lines x + y = 0 and 2 x + y + 1 = 0 3. If dv dt = g (1-v 2 k 2 ) and v = 0 if t = 0, prove that v = tanh gt k ....
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