23. Differential Equations and exp(At)
-- and lift-off on differential equations. So, this section is about how to solve a system of first order, first derivative, constant coefficient linear equations. And if we do it right, it turns directly into linear algebra. The key idea is the solutions to constant coefficient linear equations are exponentials. So if you look for an exponential, then all you have to find is what's up there in the exponent and what multiplies the exponential and that's the linear algebra. So -- and the result -- one thing we will fine -- it's completely parallel to powers of a matrix. So the last lecture was about how would you compute A to the K or A to the 100? How do you compute high powers of a matrix? Now it's not powers anymore, but it's exponentials. That's the natural thing for differential equation. Okay. But can I begin with an example? And I'll just go through the mechanics. How would I solve the differential -- two differential equations? So I'...