eng math 501e_2011 2012 fall_week1_applications

# eng math 501e_2011 2012 fall_week1_applications -...

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1 Application 1 Reduction to seperable form Find the general solution of the following equation . (2 4 5) ' 2 3 0 x y y x y - + + - + = Solution 1 2 ' (1 ') 2 2 (2 4 5) ' 2 3 0 , into . 1 (2 5). (1 ') 3 0 2 (2 5).(1 ') 2 6 0 2 5 '.(2 5) 2 6 0 4 11 '(2 5) 4 11 4 11 ' 2 5 2 5 x v v x y y y v x y y x y Write down the equation v v v v v v v v v v v v v v dv v v v dx v - = - = = - - + + - + = + - + + = + - + + = + - + + + = + = + + + = = + + 2 5 4 11 Let's 2, 4 10 2 4 11 4 11 1 2 4 11 1 2 4 11 1 2 4 11 1 2 4 11 4 Re , 2 1 2 2 4( 2 ) 11 4 8 4 v dx dv v multiply each side by v dx dv v v dx dv v dx dv dv v dx dv dv v x c v In v place it as v x y x c x y In x y x c x + = + + = + + - = + = - + = - + + = - + = - + = - - - + + = 8 4 8 11 4 8 4 8 11 y In x y c x y In x y - - - + = + + - + Application 2 Exact differential equations Solve the below equation. 2

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eng math 501e_2011 2012 fall_week1_applications -...

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