Find the solution of $(2 x - y + 1) d x + (2 y - x - 1) d y = 0.$

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} + x y + (x - y) = c .

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

x^{2} - y^{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 A $x^{2} + y^{2} - x y + (x - y) = c .$
Given $(2 x - y + 1) d x + (2 y - x - 1) d y = 0$

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

Integrating we get,

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

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

$\Rightarrow x^{2} + y^{2} - x y + (x - y) = c .$

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Find the solution of (2x−y+1)dx+(2y−x−1)dy=0.

The correct option is A x2+y2−xy+(x−y)=c.Given (2x−y+1)dx+(2y−x−1)dy=0(2x+1)(dx)+(2y−1)dy−(ydx+xdy)=0Integrating we get,∫(2x+1)(dx)+∫(2y−1)dy−∫dxy=0 ⇒x2+x+y2−y−xy=c ⇒x2+y2−xy+(x−y)=c.

Find the solution of $(2 x - y + 1) d x + (2 y - x - 1) d y = 0.$