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Hello, I am wondering if someone can look at the following:

suppose i'm given an initial value problem: dy/dt = ty(4-y)/3 with y(0) = a.

So, if I separable the variables, i would get:

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

and I would get by partial fractions

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

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

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

so can anyone tell me how I would determine how the value of the solution would vary depending on the initial value a? in other words, how could i get this into a nice form y = ....

Thanks very much.

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# Homework Help: Initial value problem

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