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I'm trying to design a parametric plot to model the effects of changing parameters on this ODE, but the plot keeps coming up completely empty. Any ideas about what's going on?

Thanks!

enter image description here

sol = DSolve[{y'[x] == y[x] (i p - r - i y[x])}, y[x], x]

With[{expr = {y[t]} /. sol}, 
Manipulate[
ParametricPlot[expr, {t, 0, 5}, 
PlotRange -> {{0, 100}, {0, 100}}], {{p, 0}, 0, 50}, {{i, 0}, 0, 
50}, {{r, 0}, 0, 50}]]

edit:added copyable code

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  • $\begingroup$ Please use copyable code instead of posting an image. $\endgroup$ – J. M.'s technical difficulties Aug 11 '17 at 15:00
  • $\begingroup$ edited in copyable code $\endgroup$ – user51632 Aug 11 '17 at 15:06
  • 2
    $\begingroup$ ParametricPlot[] is intended for parametric equations, and you do not have a parametric equation. Also, you give no initial conditions for your DE, so it can't evaluate to a number and thus be plotted. $\endgroup$ – J. M.'s technical difficulties Aug 11 '17 at 15:08
  • $\begingroup$ Darn. I know how to put in initial conditions, but do you have any advice on what type of plot I should use? I basically just want to visually compare the effects of changing the parameters. This could be in the form of many lines, or a parametric plot like this, or something I haven't thought of yet. Thanks! $\endgroup$ – user51632 Aug 11 '17 at 15:12
  • $\begingroup$ Have you tried Plot[]? $\endgroup$ – J. M.'s technical difficulties Aug 11 '17 at 15:16
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Based on J.M. remarks, and adding the constant C[1], which depends on the initial condition, as a variable alpha, this should do what you are looking for:

(* note the use of `DSolveValue` instead of `DSolve`, and the replacement rule *)
sol = DSolveValue[{y'[x] == y[x] (i p - r - i y[x])}, y[x], x] /. C[1] -> alpha
expr[p_, i_, r_, alpha_] := Evaluate@sol

Manipulate[
   Plot[expr[p, i, r, alpha], {x, 0, 5}, PlotRange -> Full], 
   {{p, 0}, 0, 50}, {{i, 0}, 0, 50}, {{r, 0}, 0, 50}, {alpha, -10, 10}
]
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