Solving Boundary-Value Problems: Find Lambda for Nonzero Solutions 🧮
Learn how to determine all values of λ in the differential equation y'' = λ y with boundary conditions y(0) = y(1) = 0 that admit nontrivial solutions. A step-by-step guide to boundary-value problems.
Dr Peyam
2.9K views • Nov 4, 2024
About this video
Boundary-Value Problems
We solve the following boundary value problem: Find all lambda for which y'' = lambda y with 0 boundary conditions has a nonzero solution. This technique involves 3 cases, depending on the roots of the auxiliary equation and features exponentials and trigonometric functions. It is extremely useful for solving partial differential equations, namely using separation of variables for the heat, wave, and laplace equation.
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We solve the following boundary value problem: Find all lambda for which y'' = lambda y with 0 boundary conditions has a nonzero solution. This technique involves 3 cases, depending on the roots of the auxiliary equation and features exponentials and trigonometric functions. It is extremely useful for solving partial differential equations, namely using separation of variables for the heat, wave, and laplace equation.
Subscribe to my channel: https://youtube.com/drpeyam
Instagram: https://www.instagram.com/peyamstagram/
Teespring merch: https://dr-peyam.creator-spring.com/?
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Video Information
Views
2.9K
Likes
127
Duration
22:33
Published
Nov 4, 2024
User Reviews
4.5
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