Question: Consider the differential equation: dy/dt = -1/2 y sin^2 t with initial condition given by y(0) = 1 Solve this equation from t = 0

Consider the differential equation: dy/dt = -1/2 y sin^2 t with

Consider the differential equation: dy/dt = -1/2 y sin^2 t with initial condition given by y(0) = 1 Solve this equation from t = 0 to t = 10 pi using the following methods: (a) Solve analytically by separating variables and integrating. (b) Solve using the Euler implicit method. Use a time step size of 0.5. (c) Solve using the 4th-order Runge-Kutta method. Once again, use a time step size of 0.5. (d) Solve using the MATLAB function ode45. (e) Compare the results for the four methods

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