Spring 08 exam 1

Spring 08 exam 1 - Mathematics 38 Examination 1...

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Mathematics 38 Differential Equations Examination 1 February 11, 2008 No calculators, notes, or books are allowed. Please make sure all electronic devices you carry are turned off and put away out of sight. Remember to sign your blue book. With your signature you are pledging that you have neither given nor received assistance on this exam. Good luck! 1. (3 points each, no partial credit) For each of the differential equations below determine the order, determine whether the differential equation is linear, and if so, whether it is homogeneous. a. t 4 d 3 x dt 3 + t dx dt - t - x 7 = 0 b. dx dt + d 7 x dt 7 = x + t 9 c. ( dx dt ) 5 + d 4 x dt 4 - t 3 x + t 7 = 0 d. x x ′′′ = x 4 x ′′ + t 5 x 2. (3 points each, no partial credit) Find all real values of α for which the given function is a solution of the given differential equation. a. x = α , d 7 x dt 7 + sin t dx dt + x - 4 = 0 b. x = α t 2 + 1 , dx dt + 2 tx 2 = 0 c. x = e αt , xx = e 2 t 3. (1 point each) For each of the following differential equations state whether it is normal on
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Spring 08 exam 1 - Mathematics 38 Examination 1...

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