question 1use runge-kutta method of order four to

Question

Question 1

Use Runge-Kutta method of order four to approximate the solution for

y' = 5y + 5t² + 2t; 0 ≤ t ≤ 1; y(0) = 1/3 ; with h = 0:1;

actual solution

y(t) = t²+ 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).