A differential equation of the form

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

Problem

\dfrac{dy}{dx}=ax^{2}+by

, with constants

a

and

b

, generates a slope field with these observed characteristics: • Along the

x

-axis (

y=0

), the slope at each point is

x^{2}

. • Along the

y

-axis (

x=0

), the slope at each point is

-y

. • At the point

(1,1)

, the slope is

0

. Determine the values of

a

and

b

, and write the resulting differential equation.