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Unformatted text preview: c . 4. [9 marks: 3 marks each] Evaluate the following: (a) dt t t ) ln( (b) d ) cos( ) ( sin 2 (c) dx x x + 2 1 2 . 5. (a) [3 marks] Show that 3 2 3 x y = is the solution of the initial value problem x y dx dy 2 = , 2 3 ) 1 ( = y . (b) [10 marks: 5 marks each] Find the general solution (whether explicit or implicit) of the following differential equations: (i) ) ln( ) 1 ( 1 t dt dy t y = + ; (ii) y x y dx dy ) 4 ( 2 2 + = . (c) [2 marks] Use your result from part (b) to find the solution to the following initial value problem: 2 ) ( , ) 4 ( 2 2 = + = y y x y dx dy . [Total: 53 marks]...
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This note was uploaded on 10/17/2010 for the course DF aadd taught by Professor D during the Spring '10 term at Clayton.
 Spring '10
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