And I'm getting these problems from page 80 of my old college differential equations books.

That's true with regular equations or differential equations.

Exact equations.

I was able to reduce this system of equations to this system of equations.

Homogeneous differential equation.

Systems of linear equations.

So the differential equations.

Let's do some more nonhomogeneous equations.

So what were linear equations?

And I won't prove some of the equations.

I have separated the equations.

In this video I want to introduce you to the idea of a polynomial.

And even within differential equations, we'll learn later there's a different type of homogeneous differential equation.

And you know how to solve the general solution of the homogeneous equation if this were 0.

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It doesn't matter what the calculations are.

linear differential equations with constant coefficients.

What does a homogeneous differential equation mean?

You're actually convoluting the functions.

People were trying to do them.

let's take equation number two.

So I will rewrite the equations.

I can explain the world around me.

learn a little bit about parametric equations.

Let's graph ourselves some inequalities.

Equations such as these are often based on the probability of each sun like star possessing an Earth like planet.

And I just used both of these equations.

Let's try to solve a more involved equation.

Solve the system of equations by substitution.

And that's why the equations look so simple.

And what's the binomial theorem?

So this first let me write down my two equations over here.

I won't go into the equations right now.

For example, factoring quadratics with

So an equal number of equations and unknowns.

And that's why parametric equations are useful.

Now I introduce you to the concept of exact equations.

So these equations can be rewritten.

We'll now move from the world of first order differential equations to the world of second order differential equations.

I would say a lot easier than what we did in the previous first order homogeneous difference equations, or the exact equations.

So what you see is that this set of parametric equations has the exact same shape of its path as this set of parametric equations.

Solve the system of equations by graphing.

I will now introduce you to the idea of a homogeneous differential equation.

So let's construct the augmented matrix for this system of equations.

least the solvable differential equations.