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Onsider the Euler equation of the functional F a) If F is independent of y, show that d -Fy" = const dx is a first integral. b) If F doos not don o

Onsider the Euler equation of the functional F a) If F is independent of y, show that d -Fy" = const dx is a first integral. b) If F doos not don o

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x1 3. Consider the Euler equation of the functional | F(x, y, y', y") dx. (a) If F is independent of show that Y, d Fy Fy" dx const is a first integral. (b) If F does not deped on x, show that F- y'(F -Fyr)-y" Fyu = const dx is a first integral.
Transcribed Image Text:x1 3. Consider the Euler equation of the functional | F(x, y, y', y") dx. (a) If F is independent of show that Y, d Fy Fy" dx const is a first integral. (b) If F does not deped on x, show that F- y'(F -Fyr)-y" Fyu = const dx is a first integral.
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