# - 2y²,y(0) =0. 1+x² 4) Consider the IVP y'= х a) Verify that y= is the...

###### Question: - 2y²,y(0) =0. 1+x² 4) Consider the IVP y'= х a) Verify that y= is the solution of this IVP. 1+x? b) Use Euler's method to numerically approximate the solution to this IVP over the interval [0,2] in x. Set the mesh width h=0.1. Calculate the true values of y atthe appropriate values of x as well as the error in your numerical approximation. Report your results in the table given. Report answers to four decimal places. Numerical Actual y % Error 0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8 c) Repeat part b with h =0.05. Numerical Actual y % Error 0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8 d) What happens to your error as you move further from your initial point. e) Which approximation is better? Why?

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