Question

Solve the logistic equation with initial conditions y1(0) = 6 and y2(0) = -3.

Answer 1

To solve the logistic equation with the given initial conditions, substitute the values into the equation and solve for the unknowns. The logistic equation with the given initial conditions is y = 12 / (1 - 2 * e^-t).

Step-by-step explanation:

To solve the logistic equation with the given initial conditions, we can use the formula:

y = c / (1 + a * e-b * t)

Substituting the initial conditions into the equation, we have:

y1(0) = c / (1 + a * e-b * 0) = 6

y2(0) = c / (1 + a * e-b * 0) = -3

Since e0 = 1, we get:

c = 6(1 + a) and c = -3(1 + a)

Solving these equations simultaneously, we find that a = -2 and c = 12.

Therefore, the logistic equation with the given initial conditions is:

y = 12 / (1 - 2 * e-t)