Use the Laplace transform to solve the given initial-value problem. y" - 3y' = 8e²t - 2e-t, y(0) = 1, y'(0) = -1 y(t) =

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Q: Use the Laplace transform to solve the given initial-value problem. y(t) = 2y"" + 3y" - 3y - 2y =…

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A: I have given the answer in the next step. Hope you understand that

Q: 3. Let f (x, y, z) = 9 (√√x² − 4y² + z² V x² +16y² + 2², where 9 is some nonnegative function of one…

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Q: Let f (x, y, z) = g (√x² − 4y² + 2²) √√x² +16y² + 2², - where 9 is some nonnegative function of one…

A: As given, f(x,y,z) = g(x2-4y2+z2) x2+16y2+z2R→(u,v) = 1+4v2cosu, v, 1+4v2sinu