The curve satisfying the differential equation ydx + (x - y)dy = 0 and passing through the point (1, 1) is: - Mathematics MCQ Mathematics Mock Test - 5 2026 | ExamTest.live

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The curve satisfying the differential equation y d x + (x - y) d y = 0 and passing through the point (1, 1) is:

Solution & Step-by-step Explanation

Rearrange the equation: y d x + x d y - y d y = 0 We recognize that y d x + x d y = d (x y) . d (x y) - y d y = 0 Integrating both sides: x y - \frac{y ^{2}}{2} = C The curve passes through (1, 1) : (1) (1) - \frac{1 ^{2}}{2} = C ⟹ 1 - \frac{1}{2} = C ⟹ C = \frac{1}{2} Substitute C back: x y - \frac{y ^{2}}{2} = \frac{1}{2} Multiply by 2: 2 x y - y^{2} = 1 ⟹ 2 x y = y^{2} + 1

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The curve satisfying the differential equation y d x + (x - y) d y = 0 and passing through the point (1, 1) is:

2 x y = y^{2} + 1

2 x y = y^{2}

x y = y^{2} + 1

2 x y = x^{2} + 1

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