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Please show each step, calculation, or math principle to arrive at the response for each prompt. I want to check my own work. (ODE stands

Please show each step, calculation, or math principle to arrive at the response for each prompt. I want to check my own work. (ODE stands for ordinary differential equation)

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Solve the following ODEs using the letordorlinearODE method. Evaluate the arbitrary constant if initial condition is provided. For these exercises you may use \\Volfraln / Alpha for complicated or tedious integrals. (a) ty' 2y 2 t4 sin(2t) t2 + 4t3 (1')) 2y' y = 4sin(3t); 31(0) 2 yo. For this question, please aISo examine how the behavior of y(t) differs for 3 cases: C 0

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