Differential Equations Lecture Work Solutions 209

Differential Equations Lecture Work Solutions 209 - 1b. uxx...

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1b. u xx + u xy + u yy + u x =0 A =1 B C 4 4= 3 < 0 elliptic dy dx = 1 ± 3 2 2 dy =(1 ± 3 i ) dx ξ =2 y (1 + 3 i ) y (1 3 i ) x α = 1 2 ( ξ + η )=2 y x β = 1 2 i ( ξ η )= 3 x α x = 1 α y α xx α xy α β x = 3 β y β xx β xy β u αα +2 u αβ ( 1) ( 3) + u ββ · 3+ u αα ( 2) + u αβ ( 2 3) | {z } u xy +4 u αα u α 3 u β
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