From the course: Complete Guide to Differential Equations Foundations for Data Science

Unlock this course with a free trial

Join today to access over 25,300 courses taught by industry experts.

Constant coefficient homogeneous second order equations

Constant coefficient homogeneous second order equations

From the course: Complete Guide to Differential Equations Foundations for Data Science

Start my 1-month free trial Buy for my team

Constant coefficient homogeneous second order equations

“

- [Instructor] In this video, you will expand upon your knowledge of working with second-order differential equations by working with constant coefficient homogenous second-order differential equations. You'll focus on learning what these equations are and be introduced to some methods on how to solve them. Let's get started. A second-order differential equation is said to be a constant coefficient homogenous second-order differential equation if it is in the form of a multiplied by y double prime, plus b multiplied by y prime, plus c multiplied by y equal to 0. This is where a, b, and c are all real constants and a must not equal to 0, but note that b and c can equal 0. In order for this equation to be homogenous, it has to equal 0 in order for it to be constant coefficient, that's where the a, b, and c come in hand. Let's solve an easy example of this type of equation. Let's look at the equation of y double prime minus y equals 0. In this case, a is equal to 1, b is equal to 0 since…

Contents