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Find the general solution of the differential equation: y dx - x dy + x*y² dx = 0.

1. x/y + x² = lambda
2. x/y + x²/2 = lambda
3. x/(2y²) + x²/4 = lambda
4. None of these

Correct answer: x/y + x²/2 = lambda

Solution

Dividing the equation y dx - x dy + x*y² dx = 0 by y²: (y dx - x dy)/y² + x dx = 0. Recognizing the exact differential d(x/y) = (y dx - x dy)/y², we get d(x/y) + x dx = 0. Integrating: x/y + x²/2 = lambda (constant).

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