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

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Identical real roots

Identical real roots

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

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Identical real roots

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- [Instructor] In the previous video, you worked with distinct real roots by solving them with the characteristic equation. But what happens if those roots are real but not distinct? In this video, you'll focus on roots that are real and identical. Let's first review what these are and how you obtain them. When solving a constant coefficient homogenous second order differential equation of the form of A multiplied by Y double prime plus B multiplied by Y prime plus C multiplied by Y equal to 0, you can then use the characteristic equation to help you solve it, which is A multiplied by R squared plus B multiplied by R plus C equal to 0. You can use factoring or the quadratic formula to solve for your roots with the formula being R equal to negative B plus or minus the square root of B squared minus 4 multiplied by A multiplied by C, divide all that by 2 multiplied by A. In this case, if B squared minus 4 multiplied by A multiplied by C equals 0, then you have two identical real roots…

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