>	restart: with(plots):with(DEtools):

Warning, the name changecoords has been redefined

>	f:=t->sqrt(t+1): defines a function

>	diff(f(t),t);

>	int(f(t),t);

>	int(f(t),t=1..7);

>

f(4);

>

evalf(%);

>	x:=subs(t=a*sin(b),f(t));

>	solve(x=6,a);

>	plot(f(t),t=0..12);

>	eqn:=diff(v(t),t)=-b*v(t)^2;

>	dsolve(eqn,v(t));

>	dsolve({eqn,v(0)=v0},v(t));

>	simplify(%);

>

>	dsolve(diff(y(t),t)=sin(t)/t^2,y(t));

>

?Ci

>	DEplot(diff(y(t),t$2)+sin(y(t)),y(t),t=0..10,[[y(0)=.5,D(y)(0)=.25]],stepsize=0.05);

>

?DEplot

>	DEplot(diff(y(t),t)=sin(t-y(t)),y(t),t=-5..5,y=-5..5);

>	DEplot(diff(y(t),t)=sin(t-y(t)),y(t),t=-5..5,y=-5..5,[[y(0)=-.25]]);

>