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: