Question

Consider the logistic equation y = y(1 - y) (a) Find the solution satisfying y₁ (0) = 6 and y₂ (0) = -4.

Answer 1

To find the solutions, substitute the initial values of y into the equation and solve for the constants. The solution satisfying y₂ (0) = -4 is y = -4.

Step-by-step explanation:

The given equation is y = y(1 - y). We need to find the solutions satisfying y₁ (0) = 6 and y₂ (0) = -4.

To find the solutions, we can substitute the initial values of y into the equation and solve for the constants. Let's start with y₁ (0) = 6:

1. For t = 0, we have y = 6.
2. Substituting into the equation, we get 6 = 6(1 - 6).
3. Simplifying, we get 6 = 6(-5).
4. This is not possible, so there is no solution satisfying y₁ (0) = 6.

Similarly, for y₂ (0) = -4:

1. For t = 0, we have y = -4.
2. Substituting into the equation, we get -4 = -4(1 + 4).
3. Simplifying, we get -4 = -4(5).
4. This equation is true, so the solution satisfying y₂ (0) = -4 is y = -4.

Therefore, the solution satisfying y₂ (0) = -4 is y = -4.