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Result of DSolve is not understood.

Posted 5 months ago
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I want to get help from Mathematica program users.

In=DSolve[y'[x] == +a*y[x]*y[x]*y[x]*(y[x] - p), y[x], x]      
Out={{y[x] -> InverseFunction[Log[#1]/p^3 - Log[-p + #1]/p^3 - 1/(2 p #1^2) - 1/(p^2 #1) &][-a x + C[1]]}}

where a and p are certain values. Even though I could get y[x], I don't know the meaning of #(Slot). I want to plot y[x]. If anyone knows, please give me answer.

Hello Sinwoo Cho,

from the documentation on Slot:

# represents the first argument supplied to a pure function.

So, e.g. Sin[#]& is the same as just Sin.

When you want to plot the result, you need to choose numerical values for all parameters,e.g.:

func = DSolveValue[y'[x] == +a*y[x]^3*(y[x] - p), y[x], x];
ReImPlot[Evaluate[func /. {C[1] -> 0, a -> -1, p -> 2/3}], {x, 1, 4}, 
 PlotRange -> All, ReImStyle -> {Red, Directive[Thick, Dashed]}, ReImLabels -> "Text"]

enter image description here

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