For the differential equation with initial condition

MATHEMATICS · Subjective · AP · Calculus BC · Differential Equations · Differential Equations

Problem

For the differential equation dydx=y(4−y)\dfrac{dy}{dx}=y(4-y) with initial condition y(0)=2y(0)=2, determine lim⁡x→∞y(x)\displaystyle\lim_{x\to\infty}y(x) and explain how the slope field supports your conclusion.

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