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0 You are given the following differential equation. dy da- - sin(.1:2) cos(y2) . c The initial condition is y = (n/E - 1)/2 at n = 0. o Solve the above differential equation numerically using the Runge-Kutta RK4 al- gorithm, from 3: = 0 to J: = 10. 0 Use it = 10000(= 104) integration steps with a stepsize h = 0.001. c Plot a chart of your solution for y(:::). (Copy and paste the chart from your graphing tool, do not include an Excel spreadsheet etc. with your submission.) I: The equation y(a:) 0.1 = 0 has a finite number of roots for a: > 0. c Find the values of the roots of the equation y(9:) 0.1 = 0 to a tolerance of Ax = 0001, using your numerical solution for 31(3) above. 0 Fill the following table with the values of the roots of the equation y(a:) 0.1 = 0, sorted in ascending order of the roots. c Write the values of the roots to 3 decimal places. root #1 (3 decimal places) root #2 (3 decimal places)