For the differential equation

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

Problem

For the differential equation dydx=(y−2)2\dfrac{dy}{dx}=(y-2)^2, investigate the behavior of the solution curve that passes through (0,1)(0,1) as xx increases. Does the slope of this curve approach zero (level off) or remain positive? State your conclusion and support it with a brief reason based on how dydx\dfrac{dy}{dx} depends on yy.

Related theory

Browse the problem library