Initials: Consider the ordinary differential equation (ODE) = f(t,y) = t - 2y. 14 (a) (2 pts) Show brief work involving

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Initials Consider The Ordinary Differential Equation Ode F T Y T 2y 14 A 2 Pts Show Brief Work Involving 1 (115.47 KiB) Viewed 39 times

Initials: Consider the ordinary differential equation (ODE) = f(t,y) = t - 2y. 14 (a) (2 pts) Show brief work involving the left-hand side and right-hand side of the ODE to confirm that the function y = t - is a solution. (b) (5 pts) In the picture below, a contour map of the right-hand side function f(t,y)=t-2y is shown. Note that all the level curves are lines and that one is darker than the rest. The one that is darker than the rest of the lines is the graph of the solution from part (a). The labels m = -4,-2,0,0.5, 2, 4 for the lines that are shown indicate the output values for f(t,y) along those lines. Here are your tasks: first draw in the slope field for = f(t, y) along these lines and then sketch at least 4 solution curves to = f(t,y). At least two solutions should be above the solution y=t- and at least two solutions should be below y=t-1. y -2 N 2 4 m=-4 m=-2 m=0 m=0.5 m=2 m=4 6 t (c) (5 pts) Show two steps of Euler's method with At = 0.5 to approximate the value of the true solution at t = 1 for the IVP = f(t,y)=t-3y, y(0) = 2. Circle your final answer. C