(Solve in R)

4. (Do this problem by computer.) Consider the initial value problem for the second-order differential equation g" +g' + 170g = 0 with initial conditions g(0) = 1 and g'(0) = -3. Solve the equation numerically and plot its graph. I suggest the following parameters: find g(x) over the interval (0,5) for 1000 uniformly spaced values of x. This means that you need to find g(x;) for x;=5i/1000 and i = 1, 2,..., 1000. I suggest that you use the method of rewriting the equation as a system of first order equations with a coefficients matrix A, then use the matrix exponential for of the solution: G(x) = exAGO, where the first entry of the column vector G(x) is g(x). Your result should consist of your R-script (if you choose to do it with R; you may use other programs if you like) and, most importantly, the graph of the solution function