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Differential Equations Lecture Work Solutions 182

Differential Equations Lecture Work Solutions 182 - z = 2 1...

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η z = 2 1 2 z 1 / 2 = 1 z η x = 1 z ξ y = 1 η y = 1 ξ xx = ( ξ x ) x = 1 z x = 1 z z z x = 1 2 z 3 / 2 = 1 2 z 3 / 2 η xx = ( η x ) x = 1 z x = 1 z z z x = 1 2 z 3 / 2 = 1 2 z 3 / 2 ξ xy = ξ yy = η xy = η yy = 0 u xx = 1 z u ξ ξ 2 z u ξ η + 1 z u η η + 1 2 z 3 / 2 u ξ 1 2 z 3 / 2 u η u yy = u ξ ξ ξ 2 y =1 + 2 u ξ η ξ y η y + u η η η 2 y =1 + u ξ ξ yy =0 + u η η yy =0 = u ξ ξ + 2 u ξ η + u η η Substitute in the equation x z 1 z u ξ ξ 2 z u ξ η + 1 z u η η + 1 2 z 3 / 2 u ξ 1 2 z 3 / 2 u η + u ξ ξ + 2 u ξ η + u η η = x 2 ( z ) 2 u ξ ξ + 2 u ξ η u η η 1 2 z 1 / 2 u ξ + 1 2 z 1 / 2 u η + u ξ ξ + 2 u ξ η u η η = z 2 4 u ξ η 1 2 z u ξ + 1 2
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