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Question 1
Use Runge-Kutta method of order four to approximate the solution for
y' = 5y + 5t^{2} + 2t; 0 ≤ t ≤ 1; y(0) = 1/3 ; with h = 0:1;
actual solution
y(t) = t^{2}+ 1/3 e^{-5t}
Question 2
Use the result of
actual solution
y(t) = t/(1+lnt)
and linear interpolation to approximate values of y(t), and compare the results to the actual values y(0:54) and y(0:94).