WEBVTT
1
00:00:00.240 --> 00:00:03.060 A:middle L:90%
the first step to solving a differential equation is to
2
00:00:03.060 --> 00:00:06.559 A:middle L:90%
find the integrating factor. So we have aged the
3
00:00:06.570 --> 00:00:09.609 A:middle L:90%
integral of p of X dx, which in this
4
00:00:09.609 --> 00:00:14.330 A:middle L:90%
case is just one D axe which gives us e
5
00:00:14.339 --> 00:00:16.780 A:middle L:90%
to the X When we integrate, the integral of
6
00:00:16.780 --> 00:00:19.070 A:middle L:90%
one would be, in this context the variable which
7
00:00:19.070 --> 00:00:22.649 A:middle L:90%
is acts. Therefore, we're now multiplying this it
8
00:00:22.649 --> 00:00:25.699 A:middle L:90%
back into the original equation. So we end up
9
00:00:25.699 --> 00:00:29.260 A:middle L:90%
with each the axe. Do you Why over D
10
00:00:29.269 --> 00:00:33.000 A:middle L:90%
backs, Plus why times eat the acts. Like
11
00:00:33.000 --> 00:00:35.350 A:middle L:90%
I said, we're multiplying all the factors by this
12
00:00:35.549 --> 00:00:37.950 A:middle L:90%
we're sending this equal to eat of the axe.
13
00:00:38.439 --> 00:00:40.649 A:middle L:90%
Now we need to solve for y right, cause
14
00:00:40.649 --> 00:00:44.969 A:middle L:90%
the question said to solve the equations or our end
15
00:00:45.210 --> 00:00:48.679 A:middle L:90%
solution is gonna be why equals something. So in
16
00:00:48.689 --> 00:00:51.240 A:middle L:90%
this context, we end up with y equals one
17
00:00:51.250 --> 00:00:53.240 A:middle L:90%
because we're dividing each of these terms by eating the
18
00:00:53.240 --> 00:00:55.490 A:middle L:90%
X. So we end up with one over here
19
00:00:55.490 --> 00:00:56.960 A:middle L:90%
because of the extra. I bet you next is
20
00:00:56.960 --> 00:01:00.960 A:middle L:90%
just one plus c and then divided by E to
21
00:01:00.960 --> 00:01:03.150 A:middle L:90%
the X, which could also be written a c
22
00:01:03.150 --> 00:01:07.590 A:middle L:90%
e to the negative x, the negative power when
23
00:01:07.590 --> 00:01:07.900 A:middle L:90%
we're writing it on one line