Question

Find a differential equation that corresponds to the given direction field.

a. y' = x - y
b. y'' = x² - y²
c. y''' = eˣ - y³
d. y'''' = sin(x) - y/x

Answer 1

The differential equation that corresponds to the given direction field y' = x - y is y' = x - y.

Step-by-step explanation:

To find a differential equation that corresponds to a given direction field, we need to determine the equation that gives the slope of the tangent line at each point.

For the direction field y' = x - y, the slope is given by the expression x - y. Therefore, the differential equation is y' = x - y.