Ask Question
23 May, 19:52

In this problem, y = 1 / (1 + c1e-x) is a one-parameter family of solutions of the first-order de y' = y - y2. find a solution of the first-order ivp consisting of this differential equation and the given initial condition. y (0) = - 1 8

+5
Answers (1)
  1. 23 May, 20:36
    0
    The solution can be determined if we can specify the value of the arbitrary constant C₁. We do this by using the initial condition. When x=0, y is equal to - 18. Substitute this to the general solution.

    y = 1 / (1 + C₁e⁻ˣ)

    -18 = 1 / (1 + C₁e⁰)

    -18 = 1 / (1+C₁)

    C₁ = - 1 - 1/18 = - 19/18

    Therefore, the specific solution is:

    y = 1 / (1 - 19e⁻ˣ/18)
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “In this problem, y = 1 / (1 + c1e-x) is a one-parameter family of solutions of the first-order de y' = y - y2. find a solution of the ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers