Question: Problem Solve the following problem over the interval from x = 0 to 1 using a step size of 0.25 where y(0) = 1.

Problem Solve the following problem over the interval from x = 0 to 1 using a step size of 0.25 where y(0) = 1. dy 33 dx = (1+2x)y (a) Analytically. (b) Euler's method. (c) Heun's method with corrector (do only one iteration for each step). (d) Midpoint method. (e) Ralston's method. (f) Fourth-order RK method (g) Display all your results on the same graph and comment on the accuracy. Develop a code or an excel sheet for the calculations.

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