Example 4: x/y

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

> de4:=diff(y(x),x) = x/y(x);

> L:=dfieldplot(de4,y(x),x=-2..4,y=-2..4,arrows=medium):

> display({L});

> dsolve({de4,y(0)=1},y(x));

> y0 := x -> sqrt(x^2+1):

> dsolve({de4,y(0.1)=0.1},y(x));

> y1 := x -> x:

> M0:=plot(y0(x),x=-2..4,colour=blue,thickness=3):

> M1:=plot(y1(x),x=-2..4,colour=yellow,thickness=3):

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

>