Question: Determine the exact solution to the initial value problem

Determine the exact solution to the initial value problem

y'(x)=   (y(x)(20-y(x)))/80 , y(0)=1

 Compute a polynomial approximation to y(x). Plot this polynomial approximation together with y(x) on the same axes for x∈[0,20]. Choose different colours and linestyles for each curve.

Investigate whether or not it is possible to choose Order to be large enough to ensure that the plots of the polynomial approximation and y(x) are indistinguishable over the [0,20] interval? If this is possible, determine the minimum value of Order required. If you think that it is not possible, explain why not.

I tried

des := diff(y(x), x) = (1/80)*(y(x))(20-y(x))

and

ics := y(0) = 1

then i type

soln := dsolve({des, ics}, {y(x)})

came up with

y(x) = RootOf(x-(Int(80/_a(20-_a), _a = _b .. _Z))+80*(Int(1/_a(20-_a), _a = _b .. 1)))

then i tried 

Y := convert(rhs(soln), polynom)

it gives me the same thing

i put

PY := plot(y, x = 0 .. 20)

then it's error...

what should I do next?