"Substitute in the dimensional variables to solve the associated dimensional problem" diff eq

[fiery briar]

What does this even mean?

I have a DE, let's say the solution is X(s) = e^s + 1. Then, I have dimensional variables x = (b/a)*X and t = s/a. I'm then supposed to substitute these into the equation to "find the solution to the associated dimensional problem". I can substitute fine, but how do I solve this?

[surreal sun]

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[vague kestrel]

@fiery briar i think it means the solution x(t)

So x(t)=b/a(e^at+1)

[fiery briar]

hey! yep, that's what it eventually meant, bit a noted I didn't realise that myself now haha

think it was just notation abuse

[vague kestrel]

Yeah just a change of variables

[vague kestrel]

Its used in fluid mechanics for example to turn navier stokes equations to non dimensional form and parameters like Reynolds number etc appear. It helps design experiments with small easier to make 3d models (like a damp or an airfoil), but equivalent to the real ones.