A. Find a general solution of the differential equation dy/dx=y2 b. Find a singular solution that is not included in the general solution.
c. Inspect a sketch of typical solution curves to determine the points (a, b) for which the initial value problem (y′)2=4y, y(a)=b

We want to solve the given differential equation, we will find:

So we have:

a) if we define:

And we derivate that, we will get:

So that is the general solution.

b) We would want a singular solution that is not included in the general form. Here we could use something like:

y = 0 we get:

dy/dx = 0 = 0^2

This is a trivial singular solution.

c) If we have y(a) = b, then:

To find the value of k we use the other condition:

y'(2) = 4*y(2)

Then we have:

So the points (a, b) are of the form: (a, 1/(9/4 - a))

If you want to learn more about differential equations you can read:

link

to determine the unit cost your would divide the total cost by the number sold.

7 bagels for $4.41       $4.41/7 = $.63 each at fresh side

5 bagels for $3.60         $3.60/5 = $.72 each at value mart