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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

See below

Step-by-step explanation:

With the information given, we only need to find the value of the parameter c1 for which the initial condition holds. Assume our solution is of the given form

Then

Thus

. Therefore, the unique solution to the initial value problem is the function

Again, it's important to note that the problem gives us the general solution for granted. If you want to solve another IVP, sometimes you need to find the general solution first, and then find the parameters corresponding to the initial conditions.

the dimensions are:

step-by-step explanation:

we want to find the dimensions of a rectangular box with volume of

we factor to obtain;

we rewrite the rightmost factor to obtain;

recall that:

we apply difference of two squares formula to obtain;

hence the dimensions are

y/x of point b= y/x of point a

step-by-step explanation:

(i got the same question, this was the correct answer.)