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steposvetlana [31]
3 years ago
9

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
Mathematics
1 answer:
fiasKO [112]3 years ago
4 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<span>)
-18 = 1/</span>(1 + C₁e⁰)
-18 = 1/(1+C₁)
C₁ = -1- 1/18 = -19/18

Therefore, the specific solution is:
y = 1/(1 - 19e⁻ˣ/18)
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3 years ago
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oee [108]
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Explanation:
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