# Fourier transformation of solution of differential equation

I'm trying to plot a Fourier transform of solution of differential equation. I have tried with:

Plot[Evaluate@
Abs[FourierTransform[
Re@Evaluate[
p[t] /. NDSolve[{p'[s] == 1 + (-1.3 + I*10 + p[s])*p[s],
p[0] == 0}, p, {s, 0, 10}, MaxSteps -> 100000]],
t, \[Omega]]], {\[Omega], 0, 100}, PlotRange -> All]


without success.

What am I doing wrong?

• The "?" button in the edit box gives tips on formatting, such as how to format code. Feb 28, 2013 at 13:21
• Why not use Fourier? ff = p[t] /. NDSolve[{p'[s] == 1 + (-1.3 + I*10 + p[s])*p[s], p[0] == 0}, p, {s, 0, 10}, MaxSteps -> 100000][[1]] and Table[ff, {t, 0, 10, 10/256}] // Fourier // Abs // Rest // Flatten // ListLogPlot[#, PlotRange -> All] & Feb 28, 2013 at 13:34

## 1 Answer

You can solve the equation analytically :

sol[s_] = DSolve[{p'[s] == 1 + (-13/10 + I*10 + p[s])*p[s], p[0] == 0}, p[s], {s}][[1, 1, 2]]

• But an analytical Fourier transform for the function seems to be still impossible? Feb 28, 2013 at 13:57
• I think so; also notice the function flattens to a constant for large argument. Feb 28, 2013 at 14:02
• Oh, that's interesting! Feb 28, 2013 at 14:17