1. Given the following initial value problem 1 <= t <= 2   y' = (y ^ 2)/(1 + t)   y(1) = - (ln(2)) ^ - 1   (h = 0.1) .   The actual solution is y(t) = - 1/(ln(t + 1))   (a) Use Runge-Kutta method of order four to approximate the solution of the given initial value problem and compare the approximations to the actual values.   (b) Use the results in (a) and Hermite interpolation to approximate value of y(t)   (c) Use the result in (b) to find the values of y(1.25) and y(1.93) Compare these approximations to the actual values.

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