Cfrgtkky

Trying to plot the 3D curve

(t,t^2,2*t^3), tin [0,1],

with the code:

begin{tikzpicture}

    begin{axis}

    %view={105}{5}, 

    [samples y=0, axis lines=center,axis on top,xlabel=$x$, ylabel=$y$, zlabel=$z$]



     addplot3+[no markers,variable=t,domain=0:1,blue,samples=80,samples y=0] (t,t^2,2*t^3);



    end{axis}



    end{tikzpicture}

I got the following output:

But I want to plot that curve in the regular coordinate system:

   begin{tikzpicture}



        draw[thick,->] (0,0,0)coordinate (O) -- (3,0,0) coordinate (X)

                node[anchor=north east]{$y$};

        draw[thick,->] (0,0,0) -- (0,3,0) coordinate (Y) node[anchor=north

                west]{$z$};

        draw[thick,->] (0,0,0) -- (0,0,3) coordinate (Z) node[anchor=south]{$x$};



    end{tikzpicture}

that is:

Which would be the code ?

Later Edit: By using view{95}{5}, the axes seem to be like in the second output, but not perfect:

begin{tikzpicture}

        begin{axis}

        [view={95}{5}, samples y=0, axis lines=center,axis on top,xlabel=$x$, ylabel=$y$, zlabel=$z$]



         addplot3+[no markers,variable=t,domain=0:1,blue,samples=80,samples y=0] (t,t^2,2*t^3);

        end{axis}

 end{tikzpicture}

The output being:

This is not an answer but an attempt to understand the question better. In your desired coordinate system, you perform a cyclic permutation of the x-, y- and z-directions, right? If that's the case, why does a change of the view and relabeling of the axes by hand not work? A brute force solution, which is certainly not a final solution, is

documentclass[border2mm]{standalone}

usepackage{tikz}

begin{document}

begin{tikzpicture}



        draw[thick,->] (0,0,0)coordinate (O) -- (3,0,0) coordinate (X)

                node[anchor=north east]{$y$};

        draw[thick,->] (0,0,0) -- (0,3,0) coordinate (Y) node[anchor=north

                west]{$z$};

        draw[thick,->] (0,0,0) -- (0,0,3) coordinate (Z) node[anchor=south]{$x$};

   defn{80} 

   foreach i in {1,...,n} {

    pgfmathsetmacro{u}{(i-1)/n}

    pgfmathsetmacro{v}{((i-1)/n)^2}

    pgfmathsetmacro{w}{2*((i-1)/n)^3}

    pgfmathsetmacro{x}{(i/n)}

    pgfmathsetmacro{y}{(i/n)^2}

    pgfmathsetmacro{z}{2*(i/n)^3}

      draw[-,blue,thick,smooth] (v,w,u) -- (y,z,x);

     }

    end{tikzpicture}

end{document}

I just posted this in order to find out whether this is the plot you want to get, and I understand that this is a hilariously complicated way of producing the plot.