This is a Matlab assignment for MAT275 (differential equation class). Please help me with the script I need to turn in for the assignment! Thank you all! :)

1. (a) If you haven't already done so, enter the following commands: f=0(t , y) (4*y) ; >> >> t=linspace(0,.5, 100); y-2*exp (4*t); % defines the exact solution of the ODE >> [t50,y50].euler(f, [0,.5] ,2, 50); % solves the ODE using Euler with 50 steps Determine the Euler's approximation for N 500 and N 5000 and fill in the following table with the values of the approximations, errors and ratios of consecutive errors att 0.5. Some of the values have already been entered based on the computations we did above Include the table in your report, as well as the MATLAB commands used to find the entries. THIS CONTENT IS PROTECTED AND MAY NOT BE SHARED, UPLOADED, SOLD OR DISTRIBUTED 2018 Stefania Tracogna, SoMSS, ASU MATLAB sessions: Laboratory 3 ratio N approximationerror 4.0216 0.5647 10.7565 50 7.1211 500 5000 (b) Examine the last column. How does the ratio of consecutive errors relate to the number of steps used? Your answer to this question should confirm the fact that Euler's method is of " order h", that is, every time the stepsize is decreased by a factor k, the error is also reduced (approximately) by the same factor (c) Recall the geometrical interpretation of Euler's method based on the tangent line. Using this geometrical interpretation, can you explain why the Euler approximations underestimate the solution in this particular example? 1. (a) If you haven't already done so, enter the following commands: f=0(t , y) (4*y) ; >> >> t=linspace(0,.5, 100); y-2*exp (4*t); % defines the exact solution of the ODE >> [t50,y50].euler(f, [0,.5] ,2, 50); % solves the ODE using Euler with 50 steps Determine the Euler's approximation for N 500 and N 5000 and fill in the following table with the values of the approximations, errors and ratios of consecutive errors att 0.5. Some of the values have already been entered based on the computations we did above Include the table in your report, as well as the MATLAB commands used to find the entries. THIS CONTENT IS PROTECTED AND MAY NOT BE SHARED, UPLOADED, SOLD OR DISTRIBUTED 2018 Stefania Tracogna, SoMSS, ASU MATLAB sessions: Laboratory 3 ratio N approximationerror 4.0216 0.5647 10.7565 50 7.1211 500 5000 (b) Examine the last column. How does the ratio of consecutive errors relate to the number of steps used? Your answer to this question should confirm the fact that Euler's method is of " order h", that is, every time the stepsize is decreased by a factor k, the error is also reduced (approximately) by the same factor (c) Recall the geometrical interpretation of Euler's method based on the tangent line. Using this geometrical interpretation, can you explain why the Euler approximations underestimate the solution in this particular example