The Bernoulli Equation // Substitutions in Differential Equations
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Open Source (i.e free) ODE Textbook: ►http://web.uvic.ca/~tbazett/diffyqs
The Bernoulli Equation is a fascinating ODE. On the surface it is a non-linear first order ODE which means we can't use the methods we have developed for first order linear differential equations. However, with a substitution u=y^(1-n), this converts into a linear ODE and then we can use the method of integrating factors. There are a lot of little substitution tricks like this one in ODEs, and we won't do most of them, but the big idea is to be always looking for ways you can convert an ODE you don't know into one you can do.
OTHER COURSE PLAYLISTS:
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► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n
►MULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd
►VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa
►LAPLACE TRANSFORM: https://www.youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1
OTHER PLAYLISTS:
► Learning Math Series
https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw
►Cool Math Series:
https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho
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Видео The Bernoulli Equation // Substitutions in Differential Equations канала Dr. Trefor Bazett
Open Source (i.e free) ODE Textbook: ►http://web.uvic.ca/~tbazett/diffyqs
The Bernoulli Equation is a fascinating ODE. On the surface it is a non-linear first order ODE which means we can't use the methods we have developed for first order linear differential equations. However, with a substitution u=y^(1-n), this converts into a linear ODE and then we can use the method of integrating factors. There are a lot of little substitution tricks like this one in ODEs, and we won't do most of them, but the big idea is to be always looking for ways you can convert an ODE you don't know into one you can do.
OTHER COURSE PLAYLISTS:
►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS
►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6
►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m
► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n
►MULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd
►VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa
►LAPLACE TRANSFORM: https://www.youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1
OTHER PLAYLISTS:
► Learning Math Series
https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw
►Cool Math Series:
https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho
BECOME A MEMBER:
►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join
MATH BOOKS & MERCH I LOVE:
► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett
SOCIALS:
►Twitter (math based): http://twitter.com/treforbazett
►Instagram (photography based): http://instagram.com/treforphotography
Видео The Bernoulli Equation // Substitutions in Differential Equations канала Dr. Trefor Bazett
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