131F06.probsess2

# 131F06.probsess2 - a b with a> 0 L-1 F as b = 1 a e-bt/a...

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Problem Session for MTH G131: 11/16/06 1). Use the Laplace transform to solve the initial value problems: y 00 + 3 y 0 + 2 y = 0 , y (0) = 1 , y 0 (0) = 0 y 00 - 2 y 0 + 2 y = e - t , y (0) = 0 , y 0 (0) = 1 2). Deﬁne f ( t ) = ± (sin t ) /t, for t 6 = 0 1 for t = 0 Find the Taylor series for f about t = 0. Assuming that the Laplace transform of this function can be computed term by term, show that L [ f ] = arctan ² 1 s ³ 3). Suppose that L [ f ] = F ( s ), show that for constants
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Unformatted text preview: a, b with a > 0, L-1 [ F ( as + b )] = 1 a e-bt/a f ( t a ) 4). Find the inverse Laplace transform of ( s-2) e-s s 2-4 s + 3 5). Find the solution of the IVP y 00 + 3 y + 2 y = u 2 ( t ) , y (0) = 1 , y (0) = 0 6). Use the convolution integral to ﬁnd the Laplace transform of f ( t ) = Z t ( t-u ) e u du...
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