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Solve dy/dx=(-5x+y)^2 -4 I got 1/6ln((u-3)/(u+3))=x using a substitution of u=(-5x+y). Is that right?

Mathematics
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the problem isnt stated properly... it looks wrong though. some clarification would help.
What do you mean?
\[dy/dx=(-5x+y)^2-4\] Is that better?

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Other answers:

That u-substitution works for this differential equation. The substitution reduces it to the variables-separable equation \[du/(u^{2}-9) + dx = 0.\]
But then you still have to integrate it, right?
Did you get the same answer I got?
Computing ...
(1/6)(ln|u - 3| - ln|u + 3| = -x + ln(C)/6 as an intermediate solution. Once that is taken back to original variables, we're finished.
My final solution is 5x - y + 3 = C e^(6x)(5x - y - 3) in implicit form.
Its explicit form is \[y = 5 x + 3(1 + C e^{6x})/(-1 + C e^{6x}).\]
For increasingly large values of x, all solution curves more closely approximate the linear function 5x + 3, so the line y = 5x + 3 is the asymtote of all solution curves.
That's a good problem, Dave :^)
I'll tell my professor;-) Thanks!
Major ten-four, good buddy :^)

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