Differential Equations Lecture Work Solutions 206

Differential Equations Lecture Work Solutions 206 - 1a....

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1a. 4 u xx +5 u xy + u yy + u x + u y =2 A =4 B =5 C =1 4 2 4 · 4 · 1=25 16 = 9 > 0 hyperbolic dy dx = 5 ± 9 2 · 4 = 5 ± 3 8 % 1 / 4 & 1 dy = dx dy = 1 4 dx y = x + cy = 1 4 x + c ξ = y = y 1 4 x ξ x = 1 ξ y η x = 1 4 η y ξ xx =0 ξ ξ xy η xx η η xy u xx = u ξξ ( 1) 2 +2 u ξη ( 1) 1 4 ± + u ηη 1 4 ± 2 + u ξ · 0+ u η · 0 u = u · 1 2 u · 1 · 1+ u · 1 2 + u ξ · u η · 0 u xy = u ( 1) · u 1 · 1+1 · 1 4 ±± + u 1 4 ± · u ξ · 0 · + u η · 0 u x = u ξ ( 1) + u η 1 4 ± u y = u ξ · u η · 1 4 u u + 1 4 u 5 u 25 4 u 5 4 u + u u + u u ξ 1 4 u η + u ξ + u η All u , u and u ξ terms cancel out
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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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