And, note that this is a fairly arbitrary functional form.

Equation

Equation

The equation that specifices how that is changing is called the equation of state.

Polar Equation

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Where's the equation?

Exact equations.

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So, I'll see you in the part 2 of using the quadratic equation.

But anyway I don't want to get caught up in terminology.

Let me write that down.

How bad was this?

But what we've said, I know you might have lost track we did all this math is we said, this equation minus 9x squared minus 9x plus 6.

Is ( 1, 7) is solution for the equations below.

Which is equal to a squared.

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It would open downward and it would go down twice as fast.

So we were able to solve this system of equations.

This is the same thing as x over x plus y over x.

I think you know how to solve them.

So that's separable.

That's what this playlist will deal with, ordinary differential equations.

So this is really the solution.

In its simplest form, it is just a multiplicative constant, usually denoted as little w.

But the more general case, is the case where it changes in time. That's called quintessence.

These are, again, probability contours.

When we say system of equations, we just mean many equations that have many unknowns.

So the first thing we want to do here is not to factor this

like a zero, but I'll try to be careful.

So there's two big classifications.

Could we measure the speed of light using the wave equation?

No? Nonlinear equations?

learned before, but it's a neat trick.

And this is a good idea to memorize.

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You might have to use a quadratic equation or something.

This is r plus 2, times r plus 3 is equal to 0.

0.2 times x is equal to 4.

Right?

Those are gonna cancel out, you're gonna be just left with 20.

This is an exact equation.

Let's say we have y is equal to 3x minus 6.

That's one of our equations.