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). Please no reposts.

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