(b) Use Laplace transform to solve the following systems of equations y' + x = e³t x' - y = 0 1 x(0) = y(0) = 1

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A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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A: Please see the below picture for detailed solution.

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A: Explanation of the answer is as follows

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A: use the substitution method to solve the integral.

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A: Given query is to find the value of the integral.

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A: NOTE: Refresh your page if you can't see any equations. . substitute (x,y)=(0,0)

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Q: Question 5 Evaluate the integral below by interpreting it in terms of areas in the figure. The areas…

A: Let's evaluate given integral.