00:01
When you start with a differential equation like this, you actually want to separate the variables.
00:08
And the only thing to do because you have the x is on the right side already is to multiply dx to the right side.
00:16
So that's called separation of variables.
00:19
So then you can integrate both sides.
00:21
And with the left side just being 1d .y, the integral of that would be y.
00:25
Notice i'm not writing a plus c right there because when i integrate the right side, 1 half x squared, and the derivative of e to the x is, e to the x, that's why the integral is also the same.
00:39
I'm just writing 1 plus c on the right side, because you can think of me subtracting a different constant over, so that's why we only write one constant.
00:48
And now we can use the initial condition that when x, x is 0, y is 4, i can just substitute into the problem...