Using Python, Consider the ODE with the following initial condition y(0) and final time T:

, ,

(a) Draw the graphs of the numerical solutions using the Forward Euler method with time step six then draw the graph of the exact solution(one figure). Print out the errors and the error orders when

(b) consider (a) using the Backward Euler Method

(c) consider (a) using the Trapezoidal Rule

- - y(0)=1 T = 1 k = 0.5 0.5 0.5 b = 0.5 o; 4 h = 0.5 0.5 0.5 0.5 0.5 = 0.50:48 16