Match the differential equation with the appropriate slope field.
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Question

Quizplus · Accepted Answer

The slope field in choice B matches the given differential equation of y' = x/(1+y^2). The slope of the lines is getting steeper as x increases, which matches the increasing derivative with respect to x in the differential equation. The slope is also getting steeper as y gets farther from 0, which matches the fact that the denominator in the differential equation (1+y^2) grows faster for larger y values, making the derivative bigger in magnitude. The differential equation y' = -x/y has slope field B because the direction of the arrows matches the behavior of the solution curves. The solution curves will be concave down near y=0 and will approach y=-inf as x->inf, which is consistent with the arrows in slope field B.

Match the Differential Equation with the Appropriate Slope Field