Solve the ODE y' = y-x-1+ 1/( x-y+2) and give the solution in implicit form.
Last edited by mr fantastic; Jul 7th 2011 at 02:20 PM. Reason: Title.
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Originally Posted by ryan1573 Solve the ODE y' = y-x-1+ 1/( x-y+2) and give the solution in implicit form. Can we see some of your work on this problem?
I really dont know how to start it . it does not fit the methods I learn in the class.
Originally Posted by ryan1573 Solve the ODE y' = y-x-1+ 1/( x-y+2) and give the solution in implicit form. Is it y' = y-x-1+ 1/( x-y+2) or y' = (y-x-1+ 1)/( x-y+2)? Big difference.
Try letting .
Originally Posted by mr fantastic Is it y' = y-x-1+ 1/( x-y+2) or y' = (y-x-1+ 1)/( x-y+2)? Big difference. I doubt it would be the second, as there is no point in writing -1 + 1 in the numerator...
dy/dx = (y-x-1)+ 1/(x-y+2) is the correct equation. it is the first one.
I try y= x+u, dy/dx= 1+ （du/dx） dy/dx = (u-2)-[1/ (u-2)]. integrating u', I have u= 0.5 u^(2) - 2u- ln(u-2). I dont know how to do next.
Originally Posted by ryan1573 I try y= x+u, dy/dx= 1+ （du/dx） dy/dx = (u-2)-[1/ (u-2)]. integrating u', I have u= 0.5 u^(2) - 2u- ln(u-2). I dont know how to do next. Hi ryan1573, You have substituted incorrectly. It should be, I hope you can continue from here.
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