30 Laplace Transform: Differential Equation Solutions Task: Refer to Question 30 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing

26 Measure Theory: Lebesgue Integral Task: Refer to Question 26 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing

A dessert store sells smoothies and ice cream. The cost for these two products is provided according to the pair of second- order linear differential equations: d²x dt² 2 +3x=2y d² y dr² +3y=2x 2 The function x(t) represents the cost of smoothies, while y(t) represents the cost of ice cream. Determine x(t) and y(t) given the following initial conditions: dx dy t = 0, x = 4, y = 2,- = O and = 0. dt dt SECOND ORDER LINEAR DIFFERENTIAL EQUATION! Use either second order/Laplace formula or what it suits. NOT eigenvalues/ eigenvectors! (20 points)