07.03 Differential Equations Mid-Module Check

Which step is necessary in verifying that lnB + 2 = −2t is a solution to dB over dt equals negative 2B?

1 over B times dB over dt equals negative 2

The differential equation y ′ = 2y will produce which of the following?

A slope field with rows of parallel tangents

A 4-kg object's position, p, is changing with respect to time, t. The object experiences a force, F, that is proportional to the object's acceleration times its mass. What differential equation represents this dynamic?

F = 4p″

Which of the following could be a slope field for the differential equation dy over dx equals tangent of x question mark

The figure presents a slope field in the x y coordinate plane. The axes are labeled from negative 5 through 5 in increments of 1. Along the y axis, the segments drawn are horizontal. Along the segments where x equals 1, there are positive slope segments and then negative slope segments where x equals 2. The segments appear to be close to horizontal but slightly negative where x equals 3.

A slope field for which of the following differential equations is shown? The figure presents a slope field in the x y coordinate plane. The axes are labeled from negative 5 through 5 in increments of 1. There is a diagonal line of positive diagonal slope segments going from quadrant 2 to quadrant 4 that separates the other segments. Above the diagonal line of segments are positive slope segments, and below the diagonal line of segments are negative slope segments.

dy over dx equals x plus y