Differential Equations Lecture Work Solutions 223

Differential Equations Lecture Work Solutions 223 - 1b. uxx...

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1b. u xx 3 u xy +2 u yy =0 A =1 B = 3 C =2 4 =9 8 = 1 hyperbolic dy dx = 3 ± 1 2 %− 2 &− 1 y = 2 x + K 1 y = x + K 2 ξ = y x ξ y η = y + x η y u x u ξ + u η u y = u ξ + u η u xx =2(2 u ξξ + u ξη )+2 u + u ηη u xx =4 u +4 u + u u xy =2( u + u )+ u + u u +3 u + u u = u u + u u xx 3 u xy u u u + u 3(2 u u + u )+2( u u + u ) = u u The solution in the original domain is then: u ( x, y )= f ( y x g ( y + x ) 223
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.

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