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midterm2sample - 18.034 Midterm #2, Sample TF Questions The...

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Unformatted text preview: 18.034 Midterm #2, Sample TF Questions The exam is Wed. 04/18/07, 1:00-1:55pm, n 1. Consider the differential equation y + a 1 y n 1 + a n y = e x . If a 1 ,a 2 ,...,a n are all positive, then every solution tend to zero as x . 2. Let 1 , 2 , 3 be three solution of y + ay + by + cy = 0 . If W ( 1 , 2 , 3 ) = 2 e 3 x , then every solution is expressed uniquely as c 1 1 ( x ) + c 2 2 ( x ) + c 3 3 ( x ) . 2 3. L [ e t ]( s ) exists for s > . 4. L [ t k ]( s ) exists for all k . 5. Let y ( t ) be the solution of the initial value problem y + 2 y + 2 y = u ( t ) with y (0) = y (0) = . (Here, u ( t ) is the unit step function.) Then, L [ y ]( s ) = 1 / ( s 2 + 2 s + s ) . 6. f ( x, y ) = x 2 | y | satisfies a Lipschitz condition on the rectangle | x | 1 , | y | 1 . 7. f ( x, y ) = xy 2 satisfies a Lipshcitz condition on the strip | x | 1 , | y | < ....
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This note was uploaded on 07/28/2008 for the course MATH 18.034 taught by Professor Hur during the Spring '07 term at MIT.

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