Welcome to week 2 of differential equations
for engineers. In this week, we'll learn about linear homogeneous
differential equations. The second-order ode has the form d squared
x dt squared plus p of t dx dt plus
q of t x equals 0. It's important that the
functions p and q do not depend on x or any
of its derivatives. These all these
commonly arise from engineering systems without
any external forces. I'll begin by generalizing the oil and numerical
method to these ode's and then develop
two theoretical ideas. The principle of superposition
and the Wronskian. We'll then tackle the
second-order homogeneous ode with constant coefficients. This ode takes the form a, d squared x dt squared plus b dx dt plus cx equals 0 where a, b, and c are constants. We'll need to discuss both the exponential and the
sine and cosine solutions of this equation. Please join me in the second week of differential
equations for engineers.