\frac{d y}{d x}=(1+4 x) \sqrt{y} (a) Using Euler's method (b) Using the Midpoint (2"d order Runge-Kutta) method (c) Using the classical Fourth-order Runge-Kutta method The exact solution of this ODE

can also be derived by using calculus as y exact (x) =1(x2 +x + 1)². Using this result, obtain the true relative error at the end of each step for all the methods. Problem 1:Solve the following problem over the interval from x = 0 to 0.5 using a step size of 0.25, wherey(0) = 1:

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