1. Solve the Initial Value Problem by using the Laplace Transform. (Show all your calculations.) y...

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1. Solve the Initial Value Problem by using the Laplace Transform. (Show all your calculations.) y" (t) 2y' (t) 8y(t) = 0 y'(0) = m, y"(0) = n where m and n are last two digits of your student ID number. 2. Find the Fourier Series for the periodic function (50 points) f(x) = (m + 1)x + n - x T where m and n are last two digits of your student ID number (50 points) m=4 and n=0 1. Solve the Initial Value Problem by using the Laplace Transform. (Show all your calculations.) y" (t) 2y' (t) 8y(t) = 0 y'(0) = m, y"(0) = n where m and n are last two digits of your student ID number. 2. Find the Fourier Series for the periodic function (50 points) f(x) = (m + 1)x + n - x T where m and n are last two digits of your student ID number (50 points) m=4 and n=0