00:01
In this question, i'm given a first order equation that is dydt is 0 .06y plus 7 ,000, with the initial condition y0 is 30 ,000.
00:15
So we want to find y in terms of t.
00:18
I'm going to bring this over as a 1 over, that is divide both sides by this.
00:27
So on the right side of left with 1.
00:29
Apply an integration sign respect to t on both sides to balance.
00:33
So on the left i have this.
00:41
The right integrating a constant one, respect to t, i'll get t plus c, where c is a constant.
00:48
Now this will fit the form of integrating 1 over ay plus b respect to y.
00:55
We'll just get lon mod of a plus b over a plus c.
01:02
So in this case i'll just get lon mod of 0 .0 6y plus 7.
01:10
Divided by 0 .06.
01:15
Now bring this up, we'll be multiplying whatever is on the right, and that will be 0 .060 plus d, where d is 0 .060.
01:35
Now i'm going to apply e to the power of whatever on both sides...