sys1 := [diff(y(x), x) = a/(1-y(x))^b+c*exp(-d*x)/(1-y(x))^2]:

dsolve(sys1)

but the result is empty.

What can I do?

The sine wave in Maple 16 is shown as following

The sine wave in Mathematica is shown as following

It's obvious that the second one is smoother than the first one,I want to know how to make curves smoother in Maple 16.

How to plot x versus theta of the following implicit function

sin(theta)-2*sin(2*x-theta+(1/3)*Pi)/sin(x+(1/3)*Pi-theta)=0

where x is the implicit function of theta

now how can I plot the relationship between x and theta(condition:-Pi<theta<Pi,-Pi<x<Pi)

How to simplify the following trigonometric expression

sin(w t-theta)+sin(w t-theta-2pi/3)-sin(w t-theta+2pi/3)

to

-2cos(w t-theta+pi/6)

I know

convert(sin(x),expln)

can convert sin(x) to expression which has "exp"

but how to produce the inverse operation?