## In Exercises 1 and 2, find the equilibrium solutions of the differential equation specified.1) dy/dt = (y + 3)/(1 – y)2) dy/dt = (t² – 1)(y²

Question

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## Answers ( )

Answer:1. Equilibrium solution: y= -3

2. Equilibrium solution y= ±1.414

Step-by-step explanation:Thinking process:

The equilibrium solution can only be derived when

1. Let’s look at the first equation:

equating to the expression gives

y + 3 = 0

y = -3

Therefore, the equilibrium solution occurs at y = -3

2. Let’s look at the second solution:

dividing each side by (t²-1) gives

1/(t²-1) = (y²-2)/ (y²-4)

factorizing the right hand side gives:

at equilibrium: , then

y² – 2 = 0

solving for y gives y = ±√2

= ±1.414