Homework 6 Problem 4 Consider the differential equation given by d²y(t) dt² + 4 dy(t) dt - +5y(t) = cos(t)u(t) with y(0)

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Homework 6 Problem 4 Consider The Differential Equation Given By D Y T Dt 4 Dy T Dt 5y T Cos T U T With Y 0 1 (73.2 KiB) Viewed 26 times

Homework 6 Problem 4 Consider the differential equation given by d²y(t) dt² + 4 dy(t) dt - +5y(t) = cos(t)u(t) with y(0) = 1, dy (0) dt 2 The goal of this probel is to solve this differential equation numerically, analytically and compare the solutions. 1. Find the exact solution (i.e. the analytical solution) y(t), t≥ 0 2. Use Euler's method to solve the differential equation with a step size h=0.001; (this is the numerical solution) 3. plot the exact solution 4. plot the numerical solution 5. Plot both solutions on the same graph.