# Solving DE Mathematica

• Mathematica

## Main Question or Discussion Point

DSolve[{x'[t] == (\[Alpha] - (x[t] - 1)^2) x[t], x[0] == 0.004}, x[t],
t]

I get the following message:
Solve::tdep: The equations appear to involve the variables to be solved for in an essentially non-algebraic way. >>

DSolve::bvnul: For some branches of the general solution, the given boundary conditions lead to an empty solution. >>

What do I do?

I need to plot the solution.

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CompuChip
Homework Helper
If you just need the plot, you can try solving it numerically.

NDSolve[{x'[t] == (\[Alpha] - (x[t] - 1)^2) x[t], x[0] == 0.004}, x[t], {t, 0, 10}]

(note how you need to specify an interval)

I get the following:

NDSolve::ndnum: Encountered non-numerical value for a derivative at t == 0.. >>

CompuChip
Homework Helper
Ah right, my mistake.
You can only solve it numerically if the entire expression is numerical. It chokes on \[Alpha] being symbolic, if you plug in a value for \[Alpha] it does work, e.g.

Code:
Block[ { \[Alpha] = 1 },
NDSolve[{x'[t] == (\[Alpha] - (x[t] - 1)^2) x[t], x[0] == 0.004}, x[t], {t, 0, 10}]
]
Will that do for you, or do you need an exact solution?

{{x[t] -> \!$$\* TagBox[ RowBox[{"InterpolatingFunction", "[", RowBox[{ RowBox[{"{", RowBox[{"{", RowBox[{"0.", ",", "10."}], "}"}], "}"}], ",", "\<\"<>\"\>"}], "]"}], False, Editable->False]$$[t]}}

I can set the value for alpha but I don't obtain a numerical solution. Then I have to plot the solution.

Hepth
Gold Member
Code:
s = NDSolve[{x'[t] == (4 - (x[t] - 1)^2) x[t], x[0] == 0.004},
x[t], {t, 0, 10}]
Plot[Evaluate[x[t] /. s], {t, 0, 10}, PlotRange -> All]`

notice you have to put in something for alpha, like previously stated. i did 4.