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**1. 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

**2. 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

**3. 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)