1. Consider the initial value problem y′ =1+y/t, y(1)=3for1≤t≤2.
• Show that y(t) = t ln t + 3t is the solution to the initialvalue problem.
• Write a program that implements Euler’s method and the 4thorder Runke-Kutta method for the above initial value problem. Useyour program to solve with h = 0.1 for Euler’s and h = 0.2 forR-K.
• Include a printout of your code and a printout of the resultsat each time step.
• Use Taylor’s method to compute w1 with h = 0.1 for orders 1through 4.
