2. [-19 Points] DETAILS This question concerns the differential equation dy dt =t-y. x=0 y=4.0 Slope Field applet. x=5 y=4.0 y=-1.0 Here is the slope field for this differential equation. You will need to print out a copy of this slope field. (Note that the graph uses x and y instead of t and y.) x=0 (a) The slope field suggests that there is a straight line solution of this differential equation. Find the equation of this straight line (your answer should be given in terms of t). y = y=-1.0 x=5 MY NOTES (b) In this part of the question, you will show that the function y = f(t) = 2et + t - 1 is a solution of the initial value problem given by the above differential equation with the initial condition y(0) = 1. Calculate formula for f(t). dy by differentiating the dt dy = dt Calculate ty by substituting for y. t-y= Simplify your answers. This shows that dy = t - y. Finally, show that the function satisfies the initial condition by calculating f(0). f(0) = dt (c) On your copy of the slope field, sketch the solution curve of the differential equation that passes through the point (0, 2). Based on the slope field, can this solution pass through the point (0.5, 2.2)? Yes No