Consider the following initial value problem 5 points (1 + t) y’ = t y (4 – y), y(0) = y0 > 0. a) solve the initial value problem and find its general solution. b) determine how the solution behaves as t ø¶. c) if the initial value y0 = 2, find the time t when the solution first reaches the value 3.99.

a) To determine its general solution we have to accommodate the differential equation:

We proceed to integrate each part as follow

Then we have:

Finally we have:

Replacing the initial value y(0) = y0, we have:

K = y0/(y0-4)

b) Please, could  you describe better what do you need because I don't understand this "t ض "

c) So we first need to find K, we replace y0=2 and we have:

K = -1

then the equation, replacing y=3.99 is:

Finally, resolving the equation we have as a result:

t = 2.84

a .4y4

hope this !