Due in blackboard final exam day. Legible single pdf. dy = (3 - v2 )sin y 1. Consider the following very non-linear initial value problem dt V(0)=-1 Use each of the following techniques and a step size of h = .05 to approximate the value of y (0.4). Although students should not round off between steps - keeping all available digits in the default mode of Excel in the interest of accuracy. In your final answer shown below, show each step in the table to four digits after the decimal point accuracy. Euler Heun Three term Taylor 4 order Technique Formula Formula Runge-Kutta 0 - 1.0000 -1.0000 -1.0000 -1.0000 05 .10 15 .20 25 30 35 .402. Use a direction fields program to plot the direction fields associated with this differential equation. Use the utility to show the particular solutions for a dozen different initial conditions - including the one in problem 1. Paste a screen capture of the results here and comment qualitatively on the long term behavior of these solutions. Use complete sentences in your narrative. Patric