Let y(t) satisfy the following 2nd order ordinary differential equation: 5y" - 2y+3y=-1, with initial conditions: y(0) = 7, y'(0) = 3. Let Y(s) represent the Laplace Transform of y(t). Then Y(s) can be represented as: (5s2 + bs + c)Y(s) = d +e+fs, S where b, c, d, e and f are constants. - The above equation for Y(s) may be rearranged to give: ps² + qs + r Y(s) = s(5s² + bs + c) where p, q and r are constants.

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A: The solution is given as

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A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

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Q: y' – y = 2te',

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Q: 6. (a) (b) Use integration or partial fractions to find the inverse Laplace transform of the…

A: The answers are given below.Explanation:

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A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

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A: We use the following standard results to solve the given problem.…

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A: We have to solve given problem: