00:01
So here we're giving that the slope, right? so the slope is just the derivative.
00:04
So d, y, dx is of the curve is, well, it's x squared, y squared.
00:14
So therefore, d, y, dx is equal to, well, x squared times y squared.
00:20
Okay, so then we can separate our variables here.
00:23
Get our dys and dxs on the same side.
00:26
So we've got y squared d .y is equal to well, x squared d x just multiplying by d x and bringing over to d x and bringing over the y's the other side so you got y squared d y is equal to x squared d x then what we know if we have a separable differential equation so we can just integrate both sides just drawing the integral on the left and on the right, we've got the integral of y squared y is equal to the integral of x squared the x.
01:07
Okay, so the integral of y squared d y, well, we've got, that's, well, negative 1 over y is equal to the integral of x squared d x.
01:25
We've got x cubed.
01:29
Over three and then plus our constant of integration, so plus c, and then we can replace, right, given the point that we're given, can replace x with negative one and y with one, and then we can solve for our constant c.
01:47
So we've got negative one over one, just negative one, minus, well, negative one cubed over three is equal to c.
02:01
So therefore we got negative one minus a negative one third.
02:06
So negative one plus one third is equal to c...