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. You are given the following differential equation. dy -- sin(x2) cos(y?). dx . The initial condition is y = (v5 - 1)/2 at x - 0. . Solve the above differential equation numerically using the Runge-Kutta RK4 al- gorithm, from r = 0 to x = 10. . Use n = 10000(= 104) integration steps with a stepsize h = 0.001. . Plot a chart of your solution for y(x). (Copy and paste the chart from your graphing tool, do not include an Excel spreadsheet etc. with your submission.) . The equation y(x) - 0.1 = 0 has a finite number of roots for > > 0. . Find the values of the roots of the equation y(x) - 0.1 = 0 to a tolerance of Ar = 0.001, using your numerical solution for y(r) above. . Fill the following table with the values of the roots of the equation y(r) - 0.1 = 0, sorted in ascending order of the roots. . Write the values of the roots to 3 decimal places. root #1 (3 decimal places) . . . ... to root #2 (3 decimal places) I