Use Euler's method to a) compute y(1), where y(x) is the solution of the initial value problem: dy + 3x²y = 6x²;y(0) = 3. Use dx = i) 1, ii) 0.1, ii) 0.01, and, iv) 0.005. Note each of i, ii, iii, and iv increases the 4. dx number of iterations by a factor of 10. A computer program would be helpful (see link in resources) b) Determine the exact solution (show your work), and c) find the error in Euler's method to compute y(1) and make a conjecture ton what happens to the error as the step size is divided by 10.

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