A one parameter family (with parameter c
) of solutions to the problem
y′=y−y2
is y=1/(1+ce−x)
(1) Find c
 so that y(−2)=−1
c=
-2/3
(2) Find c
 so that y(1)=−2
c=
-3/2



just list the final answer both of them are wrong

The correct values of \( c \) are:

1. \( c = -\frac{5}{3} \)
2. \( c = -\frac{3}{5} \)

A one parameter family (with parameter c) of solutions to the problem y' = y - y^2 is y = 1 / (1 + ce^(-x)). Find c so that y(-2) = -1 and y(1) = -2.

This problem involves solving a separable differential equation with an exponential solution and determining the parameter c based on initial conditions y(-2) = -1 and y(1) = -2. Suitable for university-level students studying differential equations.

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