Differential Equations

>>380922
>((x-1)(x-4))/dx
>/dx
>/
Is that a typo? I don't think I can solve it, but am curious. Can you post the answer? As far as a I got was doing:

dy/dx = (x(y+3)-y-3) / (x(y-2)+4y-8)

But I can't factor it in any meaningful way, was just trying to get some of the same terms you have there.

>>380938
Yeah that's a typo.
It should be ((x-1)/(x+4))dx

The answer is:
y-5ln(y+3) = x-5ln(x+4) +c

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>>380944
lol bunch of brainlets you and I.
I think it's pretty obvious how they factored it, once you work it backwards

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>>380947
Maybe not upside down this time?

>>380949
Oh, and if you're confused by the integral just do a u sub.

>>380922
Separation of variables.
https://en.wikipedia.org/wiki/Separation_of_variables

xy + 3x - y - 3 = x (y + 3) - (y + 3) = (x - 1)(y + 3)

xy - 2x + 4y - 8 = x(y - 2) + 4(y - 2) = (x + 4)(y - 2)

Then you can separate the two variables, all terms with y on one side of the equation, all terms with x on the other side.