The general solution of $(2 x - y + 1) d x + (2 y - x + 1) d y = 0$ is:

x^{2} + y^{2} + x y - x + y = c

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x^{2} + y^{2} - x y + x + y = c

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x^{2} - y^{2} + 2 x y - x + y = c

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x^{2} - y^{2} - 2 x y + x - y = c

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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Solution

The correct option is B $x^{2} + y^{2} - x y + x + y = c$
Given differential equation is

$(2 x - y + 1) d x + (2 y - x + 1) d y = 0$

$\Rightarrow 2 x d x + 2 y d y - (y d x + x d y) + d x + d y = 0$

$\Rightarrow (2 x d x + 2 y d y) - d (x y) + d x + d y = 0$

On integrating both sides, we get

$x^{2} + y^{2} - x y + x + y = c$

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