Unformatted text preview: original curves. Therefore, we have m ⊥ = F y ( x, y ) F x ( x, y ) ⇒ dy dx = F y ( x, y ) F x ( x, y ) ⇒ F y ( x, y ) dx − F x ( x, y ) dy = 0 . (b) Let F ( x, y ) = x 2 + y 2 . Then we have F x ( x, y ) = 2 x and F y ( x, y ) = 2 y . Plugging these expressions into the Fnal result of part (a) gives 2 y dx − 2 x dy = 0 ⇒ y dx − x dy = 0 . 69...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations, Trigraph, t=y t=0

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