00:01
To solve this differential equation for the given condition, we want to start by multiplying the dt over to the right side.
00:08
And then we could multiply the y over to the left side.
00:12
But then the expression t divided by t plus 1 over t, we could just rewrite that.
00:21
And actually, let's get rid of that y now.
00:24
So t divided by t is 1 plus 1 divided by t is t to the negative 1.
00:29
And this just makes taking the anti -derivative easier.
00:33
Now that we've separated variables, we got the y on the left, the t is on the right.
00:38
We'll go ahead and anti -derive.
00:41
This gives us y squared over 2.
00:43
On the right side, this gives us t.
00:48
And then, oh, well, let's see.
00:52
We could have actually just left this as 1 over t.
00:59
Over t.
01:02
So the anti -derivative of that would be plus ln absolute value of t and then plus c...
