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Unformatted text preview: F ( x, y ) d x + G ( x, y ) d y = 0. Is this equation exact? Does F/y = G/x ? If it is, nd the solution in the form W ( x, y ) = const. In all cases, even if the equation is not of a form appropriate for the method, try to make some obvious transformations which may bring it to such form. Please submit your answer to equation 10 for marking. NB: the full marks will only be awarded for all four methods, i.e. either solving equation 10 with that method or showing that the method is not applicable. 1. 1 y d y d x1 x = 0 . 2. d y d x = 23 y 3. d y d x = x 3y 3 4. xy d y d x = x 2 + y 2 5. d y d x = 3 x + 4 y + 5 4 x + 3 y + 7 6. y 3 d y d x + xy 2 = x 2 y 2 7. x 3 d y d x + y 3 = xy 8. ( x + 3 y 2 ) d y d x + y =3 x 2 9. x d y d x + y2 x = 0 . 10. * x 3 d y d xx 2 = x 2 y *...
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 Spring '10
 bikta
 Math, Differential Equations, Equations

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