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

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Various roots

Various roots

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

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Various roots

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- [Instructor] In the previous video, you learned what linear homogenous, higher order differential equations are. In this video, you will focus on solving those types of equations with constant coefficients using the characteristic equation. Let's review what this entails. Let's say you have a constant coefficient, higher order differential equation with the form of a n of minus one of t multiplied by y to the n minus one of t plus all the way to plus a1 of t multiplied by y prime of t plus a0 of t multiplied by y of t equals zero. Note that this is for real constant values for a of zero to a of n, where a n of t does not equal zero. You then have the corresponding characteristic equation, which is equal to a n of t multiplied by r to the n plus a n of minus one of t multiplied by r to the n minus one plus all the way to a1 of t multiplied by r plus a0 of t equals zero. In this video, I will have you focus on factoring the characteristic equation since other methods tend to be more…

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