I want to draw the behavior of diff equation on xy-plane, where y=x'(t)

I get many xi(t), yi(t) on different consequtive intervals. I want to draw all graphs on one picture. (But I believe there is a decision that does not use the fact that the intervals are consequtive.)

Something like

"for i from 0 to 100 do

plot(xi(t), yi(t), t=i..i+1)

end do"

How can I draw multiple graphs on different intervals on one xy-plane?

Thanks!

I have two equations, and in most cases one of them has solution, another one doesn't. In some cases both equations have solutions, and min() helps.

I have to work with a huge amount of data (in cycles) - so the decision should work in any situation.

Example:

S1 := RootFinding:-NextZero(unapply(rhs(X1)-1, t), 0.);

S2 := RootFinding:-NextZero(unapply(rhs(X1)+1, t), 0.);

SS := min(S1, S2);

The result:

Sorry for posting the question to two topics (here and there http://www.mapleprimes.com/forum/ihaveequationafterdsolvehowcaniuseonlyonepartitseewhensolutionbecomesequalsmth)

But it seems to me that it fits both of them.

________________

I have a differential equation.

ODE := diff(diff(x(t), t), t)+.2*(diff(x(t), t))-x(t) = sin(t)

ics := x(0) = .5, (D(x))(0) = 5

X1 := dsolve({ODE, ics})

So the solution is: 

I have a differential equation.

ODE := diff(diff(x(t), t), t)+.2*(diff(x(t), t))-x(t) = sin(t)

ics := x(0) = .5, (D(x))(0) = 5

X1 := dsolve({ODE, ics})

So the solution is: 

X1 := x(t) = exp((1/10*(-1+sqrt(101)))*t)*((111/404)*sqrt(101)+111/404)+exp(-(1/10*(1+sqrt(101)))*t)*(111/404-(111/404)*sqrt(101))-(5/101)*cos(t)-(50/101)*sin(t)

Now I need to find out when the solution becomes equal to 1.

But Maple of course does not understand when I write