Which of the following statements is true for the logistic differential equation

Question

Which of the following statements is true for the logistic differential equation  ? (5 points)

answer choices

	The graph has a horizontal asymptote at y = 20.
	y is growing the fastest when y = 0.
	The limiting value for y is 10.
	None of the above.

Answer 1

d y / d t = y (20 - y ) / 2

d t = 2 d y / [ y ( 20 - y ) ]

1 / 10 [ 1/y + 1 / ( 20 - y ) ] d y = d t

l n [ y ( 29 - y ) ] = 10 t + C₁

1 / 10 [ ( l n ( 1 / y ) ] + [ 1 / l n ( 20 - y ) ] = t + C₁

y ( 20 - y ) = e ^ ^{10 t + C}₁

y ( 20 - y ) = e ^ ^C₁ e ^ ^{10 t}

y ( 20 - y ) = K e ^ ^{10 t}

none of the above