Question

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?

Answer 1

the problem isnt stated properly...
it looks wrong though. some clarification would help.

Answer 2

What do you mean?

Answer 3

\[dy/dx=(-5x+y)^2-4\]
Is that better?

Answer 4

That u-substitution works for this differential equation. The substitution reduces it to the variables-separable equation
\[du/(u^{2}-9) + dx = 0.\]

Answer 5

But then you still have to integrate it, right?

Answer 6

Did you get the same answer I got?

Answer 7

Computing ...

Answer 8

(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.

Answer 9

My final solution is
5x - y + 3 = C e^(6x)(5x - y - 3) in implicit form.

Answer 10

Its explicit form is
\[y = 5 x + 3(1 + C e^{6x})/(-1 + C e^{6x}).\]

Answer 11

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.

Answer 12

That's a good problem, Dave :^)

Answer 13

I'll tell my professor;-) Thanks!

Answer 14

Major ten-four, good buddy :^)