Question: The slope field of a certain differential equation is shown. Which of the following is the solution to that differential equation?
A ) y = -1x + C
B ) y = x2 + C
C ) y = (x2+C)12
D ) y = (x3+C)13
E ) y = ln x + C
Steps to derive
1 Find the differential equations for the solutions in the options.
2 y = -1x + C, dydx = 1x2 ---------- (1)
3 y = ln x + C, dydx = 1x ---------- (2)
4 y = x2 + C, dydx = 2x ---------- (3)
5 y = (x2+C)12 , dydx = xy ---------- (4)
6 y = (x3+C)13 , dydx = x2y2 ---------- (5)
7 Draw the slope fields of the differential equations (1), (2), (3), (4) and (5) and compare with graph.
8 Slope field of dydx = xy matches the graph.
9 So, the graph is the slope field of differential equation, whose solution is y = (x2+C)12
Hence the right answer is Option C
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