I have the equation y^2=𝑎𝑥^3+𝑏𝑥^2+𝑐𝑥+𝑑.

How do I plot y against x as the coefficients a, b, c and d vary?

Thank you for your help.

I have the equation (𝑑𝑥/𝑑𝑡)^2=𝑎𝑥^3+𝑏𝑥^2+𝑐𝑥+𝑑.

How do I plot 𝑑𝑥/𝑑𝑡 against x? (as the coefficients a, b, c and d vary)

I expect it looks like the following graph:

Thank you for your help.

I have a 3D plot as follows:

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with(plots);

plot3d(sin(x*y), x = -2 .. 2, y = -2 .. 2, axes = framed, colorscheme = ["zgradient", ["Blue", "Green", "Yellow", "Red"]]);

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I want to plot its 2d contour (i.e. graph x-y plane).

How do I plot the contour of the graph in which the color of the contour lines have the corresponding colorscheme as the 3d plot?  Thank you. 

(P.S. This question has been updated)

I combined two animations as follow, but the dash line is turned into solid line. How can I solve this?

with(plots);

A := animate([X, X+t, X = -10 .. 10], t = -10 .. 10, color = red, linestyle = dash);

B := animate([X, t^2+X, X = -10 .. 10], t = -10 .. 10, color = blue, linestyle = solid);

display([A, B]);

I have two equations 

(i) x=t^2;

(ii) y=t^3;

I want to plot these two equations into a single graph [i.e. combine these two graphs: graph of x versus t (solid line, bule color), and graph of y versus t (dash line, red color)].

How do I customise the location of the legend? I want the legend located inside the blank space of graph (say, at top-right corner ) with vertical alignment. Thank you.

That is something simililar to the following graph: