10-22-11

10-22-11 - Math 5-A FALL 2011 MID-TERM PRACTICE PROBLEMS(1...

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Unformatted text preview: Math 5-A FALL 2011 MID-TERM PRACTICE PROBLEMS (1) Find the general solution of ( a ) 2 y 00- 5 y- 3 y = 0 , ( b ) y 000 + 3 y 00- 4 y = 0 , ( c ) y (4) + 2 y 00 + y = 0 . (2) Find the general solution of ( a ) y 00- 5 y + 4 y = 8 e x , ( b ) y 00 + 4 y = x cos( x ) , ( c ) y 00- 9 y + 14 y = xe 2 x + x, ( d ) y 00 + y = sec( x ) . (3) Find the solution following initial value problems ( a ) y 00 + 4 y =- 2 y ( π/ 8) = 1 / 2 , y ( π/ 8) = 2 , ( b ) y 00 + 4 y = F sin( ax ) , y (0) = y (0) = 0 , ( c ) y 00- 9 y + 14 y = xe 2 x + x, y (0) = 1 , y (0) = 0 . (4) Consider equation d 2 x dt 2 + 4 x =- 4 sin(2 t ) . (a) Find the solution satisfying the initial conditions x (0) = 0 , x (0) = 1. (b) Sketch the graph of the solution for 0 ≤ t ≤ 4 π . (c) If the function x ( t ) in part (a) is the position at time t of a mass attached to a spring, how do you describe, in your own words, the motion of the mass?...
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10-22-11 - Math 5-A FALL 2011 MID-TERM PRACTICE PROBLEMS(1...

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