restart: with(plots):with(DEtools):f:=t->sqrt(t+1);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));?CiDEplot(diff(y(t),t$2)+sin(y(t)),y(t),t=0..10,[[y(0)=.5,D(y)(0)=.25]],stepsize=0.05);?DEplotDEplot(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]]);