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Unformatted text preview: 5.) Find the general solution of the following diﬀerential equation xyy = 2 x ln( x ) . 6 6.) Consider the function(transformation) from R 2 to R 2 deﬁned by f ( ± x y ² ) = ± x 2y 2 x2 ² . a.) Find all solutions of f ( ± x y ² ) = ± ² . b.) Is f invertible? If so, ﬁnd a formula for the inverse. If not, explain why not. 7 7.) Consider the following transformations from R 2 to R 2 . Which ones are linear? Explain your answers and for those that are linear, write down the corresponding matrix. a.) f ( ± x y ² ) = ± y + x yx ² . b.) g ( ± x y ² ) = ±  x  yx ² . c.) h ( ± x y ² ) = ± x 2y 2 x 2 + y 2 ² . 8...
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 Fall '07
 McClain
 Calculus, Limits, Mathematical analysis, following improper integrals

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