Question: Let y(t) be the solution to the differential equation with the slope field as shown in Figure 2, satisfying y(0) = 0. Sketch the graph

Let y(t) be the solution to the differential equation with the slope field as shown in Figure 2, satisfying y(0) = 0. Sketch the graph of y(t). Then use your answer to Exercise 14 to solve for y(t).

2 1 0 - 1 -2 7 y -2 -1 0 12 t

Data From Exercise 14

Which of the equations (i)–(iii) corresponds to the slope field in Figure 2?

dy dt dy dt dy (iii) = y dt (i) (ii) = 1-y =1+y 2

2 1 0 -1 -2 1 /// // 1 11 11 -2 -1 0 1 2 1 t

To solve the Initial Value Problem = 1 + y, y(0) = 0, we first find the general solution of the differential

2 1 0 - 1 -2 7 y -2 -1 0 12 t

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