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

Unlock this course with a free trial

Join today to access over 24,900 courses taught by industry experts.

Real and distinct roots

Real and distinct roots

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

Start my 1-month free trial Buy for my team

Real and distinct roots

“

- [Speaker] Like I mentioned in the previous video, there are three types of roots you can gather from solving the characteristic equation. In this video, you'll focus on roots that are real and distinct. Let's first review what these are and how you obtain them. When solving a constant coefficient homogenous second order differential equation in the form of a multiplied by y double prime plus b multiplied by y prime plus c multiplied by y equal to zero, you can then use the characteristic equation of a multiplied by r squared plus b multiplied by r plus c equal to zero. You can then either factor or use the quadratic formula to solve for your roots with the quadratic formula being r equals negative b plus or minus the square root at b squared minus four, multiplied by a multiplied by c. Divide all that by two multiplied by a. In this case, if b squared minus four multiplied by a multiplied by c is greater than zero, then that means, you have two distinct real roots. If you don't want…

Contents