Differential Equations Lecture Work Solutions 213

Differential Equations Lecture Work Solutions 213 - 2 u + 5...

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1d. u xx +2 u xy +3 u yy +4 u x +5 u y + u = e x A =1 B =2 C =3 4 =4 12 = 8 < 0 elliptic dy dx = 2 ± 8 2 =1 ± i 2 y =(1 ± i 2) x + C ξ = y (1 + i 2) x η = y (1 i 2) x α = y x β = 2 x x = β 2 α x = 1 α y =1 α xx = α xy = α yy =0 β x = 2 β y =0 β xx = β xy = β yy =0 u αα ( 1) 2 +2 u αβ · 2+ u ββ · 2 +2 u αα + u αβ ( 2) +3 u αα +4 u α
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Unformatted text preview: 2 u + 5 u + u = e x 2 u + 2 u + u 4 2 u + u = e x u + u = 1 2 u + 2 2 u 1 2 u + 1 2 e / 2 213...
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