F[x_]:= Exp[-x]
F[x]

Suppose you have the diffeq

y’ = (y^((1.1)))

Then the solution is given by 

(1/(y^1.1))dy = dt,    y(0)=1

or 
(y^(-1/10 ))= (-t + c )/10  and so y = (((10/(10-t)))^10)



Plot the function  y = 1/(1-t) from -9 to 9

Plot[(10/(10-t))^(10), {t,0,9.5},PlotRange->Full]

Repeat for  0 to 9.5,  0 to 9.7, 0 to 9.9
and write down your observation in particular write down the range in each case.

Solve the problem for y’ = y^2, y(0)=1. and plot over the relevant domain.

email your results to  prcoulton@eiu.edu