Separable Eqn: y' = (xy + 3x -y -3)/(xy -2x + 4y -8)

f1player

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Feb 25, 2005
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By first separating variables, find general solutions to the following first order ODEs

y' = (xy + 3x -y -3)/(xy -2x + 4y -8)

Now however i rearrange this i cant seem to get all the x's on one side and all the y's on the other, so that i can do the integration. I've tried factoring but you still get x and y occuring together. any help on this would be great.

thanks
 
Re: Separable Equations

f1player said:
By first separating variables, find general solutions to the following first order ODEs

y' = (xy + 3x -y -3)/(xy -2x + 4y -8)

y' = (y+3)(x-1)/[(y-2)(x+4)]

(y-2)/(y+3) dy = (x-1)/(x+4) dx



Now however i rearrange this i cant seem to get all the x's on one side and all the y's on the other, so that i can do the integration. I've tried factoring but you still get x and y occuring together. any help on this would be great.

thanks
 
Try factoring and see what happens. I'll do the Numerator.

xy + 3x - y - 3 = x(y+3) - (y+3) = (x-1)(y+3)
 
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