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?

A function f is defined on R by

f(x):= (1+a|x|)^1/x      , x<0

         B                      ,  x=0

         ln(1+(a^2)|x|)/x , x>0

where α and β are constants. Investigate whether it is possible to choose α and β so
as to ensure that f is real-valued and continuous at x = 0. Compute any such values
for α and β correct to 10 significant figures. Make use of the piecewise command in
plotting a graph of any resulting continuous function(s) f over the range −20 ≤ x ≤ 20.

I used the help in Maple and manage to get 

f = piecewise(x < 0, (1+alpha*abs(x))^(1/x), x = 0, beta, x > 0, ln(1+alpha^2*abs(x))/x)

Not sure about how to compute a and B...

What does it mean by  f is real-valued and continuous at x = 0?