00:01
To find where this differential equation has a constant solutions, we'll go ahead and factor y squared out, and then we're going to set this whole thing equal to zero and so that would give us y squared, y squared minus six y then plus five and then of course from there this would factor further to y squared times quantity y minus five times quantity y minus five times quantity y minus 1.
00:38
And there are three constant solutions.
00:43
And those would be the first one.
00:46
How do we make this all equal 0? well, if y equals 0, that's one solution.
00:51
If y equals positive 5, that would make the second part 0.
00:55
And then y equals 1 would make the third part 0 as well.
01:00
So three constant solutions.
01:02
But we're going to use these now to set up intervals and then test values inside and outside of those intervals.
01:08
To find out where we have increasing and decreasing intervals as well.
01:13
Let's fan that out to five.
01:15
So let's choose test values...