Answer Happy

Problem 1. We're going to analyze the following initial value problem in three different ways: with direction fields, Euler's method and good old fashioned solving techniques! [=e="(2t - 4) y(2) = 0 a. Draw the direction field for our differential equation. Your axes should be at least 3 units in each direction (i.e. from -3 to 3 in both directions). b. Sketch the solution corresponding to our initial value. c. Use Euler's method with step size h = 0.1 to approximate values of the solution of the initial value problem at t= 1.8, 1.9, 2 and 2.1. d. Solve the given initial value problem. e. Rank your approximations from part (c) in terms of accuracy. f. Are the solutions you found over- or underestimates of the actual value? Explain this behavior in terms of the derivatives of the solution curve. g. Sketch the solution you found in part (d) and the "Euler (or tangent line) approximation" near' t = 2.