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test1 practice sol'n

# test1 practice sol'n - Math1XX3 Winter 2007 1[6 marks Find...

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Math1XX3, Winter 2007 1. [6 marks] Find the solution to the differential equation ) 2 sin( 6 2 x y dx dy = with the condition that 6 / 1 ) 0 ( = y The differential equation is separable = dx x dy y ) 2 sin( 6 1 2 c x y + - = - ) 2 cos( 3 1 c x y - = ) 2 cos( 3 1 Then, applying the condition that y=1/6 when x=0 gives 3 ) 2 cos( 3 1 + = x y McMaster University Page 1 of 10

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Math1XX3, Winter 2007 2. [6 marks] Find the most general solution to the linear differential equation x y y x 1 6 = + This equation is linear. If we rewrite it as 2 1 6 x y x y = + the integrating factor becomes 6 )) ln( 6 exp( ) 6 exp( x x dx x = = The differential equation is then 4 2 6 6 ) ( x x x y x dx d = = c x y x + = 5 ) ( 5 6 so that 6 5 1 x c x y + = McMaster University Page 2 of 10
Math1XX3, Winter 2007 3. [6 marks] Match the differential equation to the direction field (place he letter of the appropriate direction field in the space provided) i) 2 - + = x y y Field:__B ___ ii) 4 / 3 y y = Field:__A

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test1 practice sol'n - Math1XX3 Winter 2007 1[6 marks Find...

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