Question

In Problems 1 and 2,y=1/(1+c1e-x) is a one-parameter family ofsolutions of the first-order DE y'=y-y2. Find asolution of the first-order IVP consisting of this differentialequation and the given initial condition.

1. y(0)=-1/3

Answer 1

`\displaystyle y=(1)/(1-4e^(-x))`

Explanation:

`\displaystyle y=(1)/(1+C_1e^(-x))\\\\-(1)/(3)=(1)/(1+C_1e^(-0))\\\\-(1)/(3)=(1)/(1+C_1)\\ \\ 3=-1-C_1\\\\4=-C_1\\\\-4=C_1`

Thus, the specific solution to the IVP given the initial condition is
`\displaystyle y=(1)/(1-4e^(-x))`