Problem 1 [Solving ODE. See Textbook Chapter 25, especially Section 25.1 and 25.2 for related material& examples to what was covered in class] Solve the following initial value problem over the interval from t = 0 to t = 1, with y(0) =1: dy dt -+1.1y yt = 0 Start by writing down the equation y'(t) = f(t,y) that you need to solve, and clearly define the slope f(t,y). Then, for each one of the methods below, start by giving the generic formula with the subscripts i, then write that formula at each iteration with the corresponding value of i (=0,1,...), and finally show which numbers you are plugging in that formula at each iteration. a) Using Euler's method with h = 0.5 b) Using Heun's method with h = 0.5 c) Using the midpoint method with h = 0.5 HINT: As h=0.5, You only need to write the first two iterations (i.e. for t=0.5 and t2=1).