Direction Fields and Euler’s Method

Match the differential equation with its direction field (labeled I–IV). Give reasons for your answer.

Match the differential equation with its direction field (labeled I–IV). Give reasons for your answer.

[3] y^’=2-y

When you have a derivative, when it is equal to zero, it has a horizontal tangent.

When y=2 we will have horizontal tangents

The direction filed II is the correct graph because graph II, IV do not have horizontal slopes at y=2 and graph I has horizontal slopes everywhere y=0. This leaves III as the correct answer.

[4] When y=2 or x=0 we have horizontal tangents. This leaves I.

[5] When x+y=1, we have horizontal tangents. Plot the line x+y=1 and this is IV

[6] Check slopes but clearly this is II.