Question: solve these question 3. Develop the formula for the Laplace transform of eat. Hint: Begin by stating the definition. Explain any conditions and assumptions you

solve these question

3. Develop the formula for the Laplace transform of eat. Hint: Begin by stating the definition. Explain any conditions and assumptions you make in your development.5. Find a solution to the given initial value problem(s) using Laplace transforms. Show your work leading to the solution. You may use a table of Laplace transforms to help you. Hint: Check your results by matching to your solution obtained by the method of undetermined coefcients. (a) y\" y = $1110?) - 62t; W) = 1, y'(0) = 1 (b) y\" = 6t; y(0) = 3, y'(0) = 1 (C) y\" + 9y = 27; 11(0) = 4, y'(0) = 6

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