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In this problem, y = 1/(1 + c1eāˆ’x) is a one-parameter family of solutions of the first-order de y' = y āˆ’ y2. find a solution of the first-order ivp consisting of this differential equation and the given initial condition. y(0) = āˆ’ 1 8

Respuesta :

meerkat18
The solution can be determined if we can specify the value of the arbitrary constant Cā‚. 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 + Cā‚eā»Ė£)
-18 = 1/(1 + Cā‚eā°)
-18 = 1/(1+Cā‚)
Cā‚ = -1- 1/18 = -19/18

Therefore, the specific solution is:
y = 1/(1 - 19eā»Ė£/18)

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