First Order Diff. Eqn w/ Inital Value

[aznkid310]

Homework Statement

dy/dt = ty(4-y)/3

y(0) = y_o

Suppose y_o = 0.5. Find the time T at which the solution first reaches the value 3.98

Homework Equations

I separated, integrated and solved, so do i just plug in y_o wherever i see y and 0 for t to find the constant C and plug this back into my original solution? I must've got the wrong solution b/c my answer is not correct. Also, is my integral correct? I wasn't sure how to do it

The Attempt at a Solution

dy/[y(4-y)] = t/3 dt

After integrating both sides:

(1/4)( ln(y) - ln(y-4) ) = (t^2)/6 + C

Aftering combining logs and exponentiating both sides:

y/(y-4) = e^((2t^2)/3 + 4C)

 

[HallsofIvy]

Well, what about the rest of it? What did you get for C? What was your final answer?