Question: The slope field in Fig. 4(a) suggests that the solution curve of the differential equation y = t - y through the point (0, -1)

The slope field in Fig. 4(a) suggests that the solution curve of the differential equation y′ = t - y through the point (0, -1) is a straight line.

y 3 N [ |||||| 0 1 2 3 4 (a) Slope

(a) Assuming that this is true, find the equation of the line.

(b) Verify that the function that you found in part (a) is a solution by plugging its formula into the differential equation.

y 3 N [ |||||| 0 1 2 3 4 (a) Slope field of y = t - y. t

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