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You can combine plots in Maxima with the command "xfun" inside plotdf e.g.

plotdf([x+y,x/2+y], [xfun,"-0.7071*x;0.7071*x"])$

In you case:

plotdf(4*y/x+x*sqrt(y),[xfun,"x^4*(log(x)+2)^2/4"],
[trajectory_at,1,1],[x,0,4],[y,0,10])$

you can use several functions inside the quotes, separated by semi colons.

Daniel