{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

midterm2sample

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 &amp;gt; . 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 | &amp;lt; ....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online