The general solution of the differential equation d y d x = x y + x - 2 y - 2 x y - 2 x + y - 2 is

Question

The general solution of the differential equation d y d x = x y + x - 2 y - 2 x y - 2 x + y - 2 is, x + y + 3 log x + 1 y + 1 = c, x + y + 3 log y + 1 x + 1 = c, x - y + 3 log x + 1 y + 1 = c, x - y + 3 log y + 1 x + 1 = c

MARKS App · Accepted Answer

d y d x = x y + x - 2 y - 2 x y - 2 x + y - 2 d y d x = x - 2 y + 1 x + 1 y - 2 y - 2 y + 1 d y = x - 2 x + 1 d x y + 1 - 3 y + 1 d y = x + 1 - 3 x + 1 d x d y - 3 y + 1 d y = d x - 3 x + 1 d x Integrating on both sides, we get y - 3 ln y + 1 = x - 3 ln x + 1 + c x - y + 3 log y + 1 x + 1 = c

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