linear differential equation with a constant coefficient.

And this works every time for second order homogeneous constant coefficient linear equations.

I could just create a coefficient matrix, where the coefficient matrix would just be, let me write it neatly, the coefficient matrix would just be the coefficients on the left hand side of these linear equations.

And the binomial expansion of this I'll use that combinatorics or that binomial coefficient notation.

So like we've done in every one of these constant coefficient linear second order homogeneous differential equations, let's get the characteristic equation.

In general when we first thought about these linear constant coefficient differential equations, we said, well e to rx might be a good guess.

Coefficient.

Real coefficient

Imaginary coefficient

leading coefficient.

And notice this coefficient is the same as that coefficient.

And one of the linear combinations of these guys is you just set the coefficient on a1 to be 1, and the coefficients on everyone else to be 0.

Linear

linear

Linear

linear

linear

Linear

Linear

Linear

Linear

It's not linear. And our intuition is linear.

And then, is this linear or non linear?

China s coefficient is 0.47.

Target values Gini coefficient

That's the fifth coefficient.

What's the sixth coefficient?

This coefficient becomes 4.

The coefficient is 1.

If we can't get a 1 coefficient, we'll at least have a lower coefficient here.

Times its coefficient times the fifth term's coefficient divided by 5, for the fifth term.

The leading coefficient of the first row is 1 2 is the leading coefficient of the second row 4 is the leading coefficient of the third row, and the last row does not have a leading coefficient.

Linear Spline

Linear Sweep

Random Linear

Linear motion

Linear B

Linear Scale

Bi Linear

linear transformation.

linear transformation.

linear combination.

linear combination.

linear transformation.

linear regression.