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Select one among multiple solutions that satisfies a certain condition and 3D Plot it with varying simulation values

Mathematica Asked by ppp on January 4, 2021

My function is as follows:

$$f(x)=ax^5+bx^4+cx^3+dx^2+ex+g=0$$

Since it does not generate an analytical solution, I tried to do a simulation exercise as follows.

Simulation values: $a=-2$, $b=3$, $c=5$, $g=3.5$.

And for $0leqslant dleqslant 1$ and $0leqslant eleqslant 1$, among five different solutions, I would like to pick the one that is real and positive, and 3DPlot it against $d$ and $e$.

My Mathematica code is as follows:

Plot3D[x/.sol=Select[{Solve[ax^5+bx^4+cx^3+dx^2+ex+f==0,x]},#>0&,1],{d,0,1},{e,0,1}]

And the result I get is this:

enter image description here

Any help would be greatly appreciated!

2 Answers

This may be close to what you want.

a = -2;
b = 3;
c = 5;
g = 3.5;

tab = Table[
  x /. Solve[a x^5 + b x^4 + c x^3 + d x^2 + e x + g == 0, x, 
     Reals][[1]], {d, 0, 1, .1}, {e, 0, 1, .1}];

ListPlot3D[tab, DataRange -> {{0, 1}, {0, 1}}, AxesLabel -> {d, e}]

enter image description here

Answered by Bill Watts on January 4, 2021

With[{a = -2, b = 3, c = 5, g = 35/10},
  sol = Solve[{a x^5 + b x^4 + c x^3 + d x^2 + e x + g == 0, 0 <= d <= 1, 0 <= e <= 1}, x, Reals]
]

Plot3D[
  Evaluate[x /. sol],
  {d, 0, 1}, {e, 0, 1}
]

Mathematica graphics

Answered by MarcoB on January 4, 2021

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