"How to solve Repeated Eigenvalues of Systems of Differential Equations : Case Three"

Описание: "How to solve Repeated Eigenvalues of Systems of Differential Equations : Case Three"

In this comprehensive video, I will walk you through the process of solving systems of differential equations that involve repeated eigenvalues, providing you with a clear and detailed step-by-step approach.
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There are three cases of repeated eigenvalues:
Case Three: In this case the eigenvalues r repeated 3 times but it produces only one eigenvector U1, then in that case we can find generalized eigenvector U2 and U3 for r by using (A-rI)U2=U1 and (A-rI)U3=U2 and the solutions corresponding to r are : U1e^(rt) and (U1t+U2)e^(rt) +(U1t/2! +U2t+U3)e^(ret)

Repeated eigenvalues can present unique challenges when solving systems of differential equations, but fear not! This video is designed to demystify the process and equip you with the skills to tackle these situations with confidence.

Throughout the video, we will break down the steps involved in solving systems of differential equations with repeated eigenvalues, explaining the underlying concepts and providing practical examples to illustrate each stage. By the end of this tutorial, you will have a solid understanding of how to approach and solve these types of systems effectively.

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