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Algebraic Identities

Find the solu...

Question

Find the solution of
$(x + 2 y - 2) d x + (2 x - y + 3) d y = 0.$

x^{2} - y^{2} - 4 x y - 4 x + 6 y = k .

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x^{2} - y^{2} + 2 x y - 4 x + 6 y = k .

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

x^{2} - y^{2} - 2 x y - 4 x + 6 y = k .

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

x^{2} - y^{2} + 4 x y - 4 x + 6 y = k .

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Solution

The correct option is D $x^{2} - y^{2} + 4 x y - 4 x + 6 y = k .$
Given equation can be written as,
$(x - 2) d x - (y - 3) d y + 2 (y d x + x d y) = 0$
Integrating we get,
$\frac{x^{2}}{2} - 2 x - \frac{y^{2}}{2} + 3 y + 2 x y = c$
$\Rightarrow x^{2} - y^{2} + 4 x y - 4 x + 6 y = k .$

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