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Question: The slope field of a certain differential equation is shown. Which of the following is the solution to that differential equation?



A ) y = e- x + C
B ) y = ln x + C
C ) y = - cos x + C
D ) y = ex + C
E ) y = sin x + C

Steps to derive

1 Find the differential equations for the solutions in the options.

2 y = e- x + C, dydx = - e- x ---------- (1)

3 y = ln x + C, dydx = 1x ---------- (2)

4 y = - cos x + C, dydx = sin x ---------- (3)

5 y = ex + C, dydx = ex ---------- (4)

6 y = sin x + C, dydx = cos x ---------- (5)

7 Draw the slope fields of differential equations (1), (2), (3), (4) and (5) and compare with graph.

8 Slope field of dydx = ex matches the graph.

9 So, the graph is the slope field of differential equation, whose solution is y = ex + C.



Hence the right answer is Option D

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