hmk1 - y 00 + 2 y + y = e-4 t , y (0) =-15 16 , y (0) = + 1...

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Math 267 : Homework 1 Due January 12, 2011 1. Find the general solution of the following DEs. (a) y 00 - 2 y 0 = 0, (b) y 00 + 5 y 0 + y = 0, (c) x 2 y 0 = y 2 + xy , [ Hint: start with the substitution u = y/x . ] 2. Solve the following IVPs and sketch the solutions. (a) y 00 - 5 y 0 + 6 y = 0 , y (0) = 0 , y 0 (0) = 1 . (b) y 00 + 4 y = 0 , y ( π/ 8) = 2 , y 0 ( π/ 8) = - 4 . (c) ( t 2 y 0 + 4 ty - y 3 = 0 , y (1) = 1 . [ Hint: start with the substitution v = y - 2 ] 3. Find the general solution of,
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Unformatted text preview: y 00 + 2 y + y = e-4 t , y (0) =-15 16 , y (0) = + 1 16 . 4. Find all real values 0 < < 2 for which the problem below has a non-zero solution. y 00 + y + y = 0 , y 2 = 0 , y (0) = 0 . 1...
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