Given that the differential equation dy/dx = (x+y+2)/(x+y+1), by using a suitable substitution to reduce it to a differential equation with separable variable.

How do I get a suitable substitution for this? Any method can be used?

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- April 22nd 2013, 08:05 PMalexander9408Substitution method
Given that the differential equation dy/dx = (x+y+2)/(x+y+1), by using a suitable substitution to reduce it to a differential equation with separable variable.

How do I get a suitable substitution for this? Any method can be used? - April 23rd 2013, 04:30 AMchiroRe: Substitution method
Hey alexander9408.

You should first try using the fact x + y + 2 = x + y + 1 + 1 so you will get 1 + 1/(x+y+1).

I'm not sure what kind of DE this is though. If you need an analytic result or can you use a numerical scheme? The DE should be very close to f(x) = x since (x+y+2) is almost equal to (x+y+1) for large enough |x+y|. - April 23rd 2013, 04:51 AMProve ItRe: Substitution method