The slope field for y \' = 0.5(1 + y)(2 ? y) is shown in the figure below. Find

Question

The slope field for y ' = 0.5(1 + y)(2 ? y) is shown in the figure below.

Find the equilibrium solutions and state whether they are stable or unstable.

(smaller value)y= _______ is a(n) Stable/Unstable equilibrium.

(larger value)y= _______ is a(n) Stable/Unstable equilibrium.

The slope field for y ' = 0.5(1 + y)(2 ? y) is shown in the figure below. Find the equilibrium solutions and state whether they are stable or unstable. (smaller value)y= _______ is a(n) Stable/Unstable equilibrium. (larger value)y= _______ is a(n) Stable/Unstable equilibrium.

Explanation / Answer

Given equation is y ' = 0.5(1 + y)(2 y).
Apply Integral on both sides we get the solution is
y2(y+1.5)=0

then y=0 or y=-1.5.

(smaller value)y= -1.5 is a(n) Unstable equilibrium.

(larger value)y= 0 is a(n) Stable equilibrium.

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