A slope field is generated by the differential equation dy dx =(ax+b)(y+2)

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

Problem

A slope field is generated by the differential equation

\frac{dy}{dx}=(ax+b)(y+2),

where

a

and

b

are constants. The field shows horizontal segments along

y=-2

. In addition, the slope at

(0,-1)

4

and the slope at

(3,-1)

10

. Determine the explicit expression for

\dfrac{dy}{dx}

by finding

a

and

b