> 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);

[Plot]

> 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);

[Plot]

> ?DEplot

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

[Plot]

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

[Plot]

>