Solve :
$(3 y - 7 x + 7) d x + (7 y - 3 x + 3) d y$ =0

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Solution

Given,

$(3 y - 7 x + 7) d x + (7 y - 3 x + 3) d y = 0$

$(3 y) d x - (7 x) d x + 7 d x + (7 y) d y - (3 x) d y + 3 d y = 0$

Upon integration, we get,

$3 y x - \frac{7}{2} x^{2} + 7 x + \frac{7}{2} y^{2} - 3 x y + 3 y = 0$

$7 x + 3 y - \frac{7}{2} (x^{2} - y^{2}) = 0$

$7 x + 3 y = \frac{7}{2} (x^{2} - y^{2})$

$14 x + 6 y = 7 x^{2} - 7 y^{2}$

$7 x^{2} - 7 y^{2} - 14 x - 6 y = 0$

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Similar questions

(3 x - 7 x + 7) d x + (7 y - 3 x + 3) d y = 0

(3 y - 7 x + 7) d x + (7 y - 3 x + 3) d y = 0

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3 x + 7 y = 32

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\frac{d y}{d x} = \frac{3 y - 7 x + 7}{3 x - 7 y - 3}

(6 x + 7 y - 4) d x + (7 x - 4 y + 3) d y = 0

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