Then a letdey e constantsyand e 0 a ux ux

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Unformatted text preview: ave p 7. From the Course Notes b2 105 we have p. 4ac ⇠x b p = and ⇠y b ⇠x b 2a2 4ac = and a with ⇠y = 0 ⇠y ⌘y = 0. 2Thus and p ⌘x b + b2 p = ⌘y b ⌘x b + 2a2 = ⌘y 2a 4ac 4ac with ⇠y = 0 and ⌘y = 0. Thus x ⌘x ⇠ ⇠x ⌘x B = ⇠y ⌘y 2a +b + + 2c ⇠y ⌘y ⇠y ⌘y ⇠x ⌘x ⇠x ⌘x B = ⇠y ⌘y 2a 2 + b + + 2c ⇠yb⌘y (b2 ⇠y ac)⌘y 4 b = ⇠y ⌘y 2a 2 +b + 2c 22 ab b (4a 4ac) b = ⇠y ⌘y 2a 2 +b + 2c 4a2 a b + 2c = ⇠y ⌘y 2c a2 b + 2c = ⇠y ⌘y 2c 2 ba = ⇠y ⌘y 4c . a2 b = ⇠y ⌘y 4c . This is nonzero since b2 4ac > a , ⇠y = 0 and ⌘y = 0. 0 This is nonzero since b2 4ac > 0, ⇠y = 0 and ⌘y = 0. ⇠x ⌘x ⇠x ⌘y ⇠y ⌘x = ⇠y ⌘y ⇠y ⌘y ⇠x ⌘x p p ⇠x ⌘y ⇠y ⌘x = ⇠y ⌘y ⇠yb ⌘yb2 4ac b + b2 4ac p p = ⇠y ⌘y b 2a2 4ac b + 2a2 4ac b b p = ⇠y ⌘y 2 2a ac 2a b 4 p = ⇠y ⌘y . b2 a 4ac = ⇠y ⌘y . a This is nonzero since b2 4ac > 0, ⇠y = 0 and ⌘y = 0. This is nonzero since b2 4ac > 0, ⇠y = 0 and ⌘y = 0. 8. Consider the PDE 6. Consi...
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