ODEs - Seperable differential equation, is an explicit answer necessary in an exam? Find the general solution for the following first order differential equation:
$$\frac{dy}{dt}=(1-y)(3-y)(5-t).$$
I end up getting to
$$\exp(10x-x^2+2C)=(y-3)(y-1).$$
Is there any more simplifying that can be done to express $y$ explicitly? Wolfram Alpha has an explicit answer, but that may be due simply to its computational power...
Do you think it is likely, that in an exam, it is required to simplify further?

i think you made a sign error. separating the equation you get $$\dfrac{dy}{(1-y)(3-y)} = (5-t)dt$$  the partial fraction decomposition gives you $$\dfrac{dy}{y-3} - \dfrac{dy}{y-1} = (10 - 2t)\ dt$$ on integration this gives you 
$$\dfrac{y-3}{y-1} = Ce^{10t -t^2}$$ 
solving the last one for $y$ gives $$y = \dfrac{3-Ce^{10t-t^2}}{1+Ce^{10t-t^2}} $$
