MATLAB

dt = dt Q2. The Explicit Euler Formula: Let user = F(t, S(t)) be an explicitly defined first order ODE with interval (to ty] with spacing h. Without loss of generality, assume that to = 0 and t; = Nh for some positive integer values N. The linear approximation of S(t) around t; and tj+1 is given by ds(t) s(tj +1) = s(t)+ (tj+1 tj) or equivalently s(tj+1) = s(t)+F(t;}S(t;) Consider the differential equation = &-+ with initial condition fo = -1 has the exact solution f(t) = -6*. Use MATLAB code to 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 df(t) dt Q3. Given the following discrete time equation y[n] +avin 11 -- vin 2] = x[n] Assume the initial values w[0]=0; y[-1)=0. Solve the given equation and plot the graph. Present the work in MATLAB. 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. Write the MATLAB code to perform the task