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Differential Equations Lecture Work Solutions 4

Differential Equations Lecture Work Solutions 4 - 5 u =...

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Unformatted text preview: 5. u = F (xy ) + x G ux = y F (xy ) + G y x y x − uxx = y 2 F (xy ) + − y G x2 y x +x − y x uxx = y 2 F (xy ) + y x y G x2 y x2 G y2 G x3 y x y G x2 y x y x − 1 uy = x F (xy ) + x G x y x 1 G x + y x uyy = x2 F (xy ) + x2 uxx − y 2 uyy = x2 y 2 F + y2 G x3 − y 2 x2 F + 1 G x Expanding one finds that the first and third terms cancel out and the second and last terms cancel out and thus we get zero. 4 ...
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