Tangent

> detan:=diff(y(x),x) = 1 + y(x)^2;

> L:=dfieldplot(detan,y(x),x=-1..2,y=-4..8,arrows=medium):

> display({L});

> dsolve({detan,y(0)=0},y(x));

> y0 := x -> tan(x);

> dsolve({detan,y(0)=0.5},y(x));

> y1 := x -> tan(x+.4636476090);

> M0:=plot(y0(x),x=-1..1.55,colour=blue,thickness=3):

> M1:=plot(y1(x),x=-1..2,colour=yellow,thickness=3):

> display({L,M0,M1});

>