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Assignment 2 01. Given that the function yi= 12 sin(10x + 5) and y2 = x-1001 Plot y1 for 0 sx s5 and y2 for -6 5x5 6 on the same figure (divided into two sections) Indicate clearly the graph components. d) dt Q2. The Explicit Euler Formula: Let F(t, S(:)) be an explicitly defined first order ODE with interval (to.tz with spacing A. Without loss of generality, assume that to = 0 and ty = Nh for some positive integer values N. The linear approximation of S(t) around and ty+1 is given by ds() s(t-1) = $() + (t+1-4) dr or equivalently st:1) = s(t) + F(S) aro Consider the differential equation =e! with initial condition o = -1 has the exact solution f(1) =-e-. Approximate the solution to this initial value problem between 0 and 1 in increments of 0.1 using the Explicit Euler Formula. Then, plot the difference between the approximated solution and the exact solution. dt Q3. Given the following discrete time equation vn+ vn 1 - y - 2) = x[n] Assume the initial values y[0=0; y[-11-0. Solve the given equation and plot the graph. Q4. Determine how long it will take to accumulate at least $10,000 in a bank account if you deposit $500 initially and $500 at the end of each year, if the account pays 5% annual interest