L14 - Euler Equations Consider the Euler Equation L y def =...

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Unformatted text preview: Euler Equations Consider the Euler Equation L [ y ] def = x 2 y 00 + αxy + βy = 0 . ( E ) Every point x 6 = 0 is an ordinary point, since P ( x ) = x 2 6 = 0 . But x = 0 is not an ordinary point, but rather a singular point , since P (0) = 0 . But x = 0 may be the point of interest. What to do? Euler Equations Consider the Euler Equation L [ y ] def = x 2 y 00 + αxy + βy = 0 . ( E ) Every point x 6 = 0 is an ordinary point, since P ( x ) = x 2 6 = 0 . But x = 0 is not an ordinary point, but rather a singular point , since P (0) = 0 . But x = 0 may be the point of interest. What to do? Try y = x r . What is x r ? What is its derivative? Euler Equations Consider the Euler Equation L [ y ] def = x 2 y 00 + αxy + βy = 0 . ( E ) Every point x 6 = 0 is an ordinary point, since P ( x ) = x 2 6 = 0 . But x = 0 is not an ordinary point, but rather a singular point , since P (0) = 0 . But x = 0 may be the point of interest....
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This note was uploaded on 09/07/2010 for the course PHY 303L taught by Professor Turner during the Spring '08 term at University of Texas.

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L14 - Euler Equations Consider the Euler Equation L y def =...

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