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M427Kprac2

# M427Kprac2 - many terms as you like ’cause heck it’s a...

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M427K Sample test 2 Sec’s 3.6 to 6.5, 10.1 1. Find the general solution of y 00 + 2 y 0 + y = e - t t 3 . 2. A 5 kg. block stretches a spring 2 meters. The block is attached to a mechanism which has has a damping constant of 3 ( N · s/m ) and is acted on by an external force of 2 sin(3 t ). The mass is pulled down a distance of 1.5 meters and given an initial upward velocity of 6 m/s. Find the position of the block after 1 minute. 3. Find the first 4 nonzero terms of the series solution about x 0 = 0 to the IVP (1 - x ) y 00 + xy 0 - 2 y = 0 , y (0) = 0 , y 0 (0) = 1 . 4. Tell whether 0 is a regular singular point of xy 00 + y 0 - y = 0 and if so, find the series solution centered there. (As many terms as you like, ’cause, heck, it’s a sample test.)
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Unformatted text preview: many terms as you like, ’cause, heck, it’s a sample test.) 5. Let f ( t ) = 3 for 0 ≤ t < 2 and f ( t ) = t for 2 ≤ t < 4 and f ( t ) = 0 if t > 4. Find L { f ( t ) } . 6. Find L-1 ‰ 6 e-3 s s 2 + 4 ± . 7. Use Laplace transforms to solve the IVP: y + y = sin( x ) ,y (0) = 1 . 8. Express the function in problem 5 in terms of unit step functions. 9. Solve the IVP y 00 + 4 y + 5 y = 3 δ ( t-2)-2 δ ( t-3) , y (0) = 0 , y (0) = 0 . 10. Find the eigenvalues and corresponding eigenfunctions to the BVP y 00 + λy = 0 , y (0) = 0 , y (3) = 0....
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