A slope field is produced by a differential equation of the form

MATHEMATICS · Subjective · AP · Calculus AB · Differential Equations · Differential Equations

Problem

\dfrac{dy}{dx}=ax+by

, where

a

and

b

are constants. It is observed that: • Every line segment on the line

y=-x

is horizontal. • At the point

(0,2)

, the slope is

-6

. Determine the values of

a

and

b

, and state the differential equation.