Consider the differential equation dy/dt = 2 √ |y|. (a) Show that the function y(t) = 0 for all t is an equilibrium solution.

(b) Find all solutions. [Hint: Consider the cases y > 0 and y < 0 separately. Then you need to define the solutions using language like "y(t) = . . . when t ≤ 0 and y(t) = . . . when t > 0."]

(c) Why doesn’t this differential equation contradict the Uniqueness Theorem?

(d) What does HPGSolver do with this equation?

answer:

the position of equilibrium will shift to the left.

step-by-step explanation:

the general equation for the dissociation of a weak base is

b + h₂o   ⇌   bh⁺ + oh⁻

according to le châtelier's principle, when a stress is applied to a system at equilibrium, the system will respond in a way that tends to relieve the stress.

if you apply a stress by adding more bh⁺ or oh⁻,   the system will respond by moving in a direction that gets rid of the added ions.

the position of equilibrium will shift to the left, forming more of the undissociated base.

2x^2+5x+17

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