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By writing the equation as the exact differential of an expression in x and y, find the general solution of (2x³ - x y²) dx + (2y³ - x² y) dy = 0.
- x⁴ - x² y² + y⁴ = c
- x⁴ + x² y² - y⁴ = c
- x⁴ - x² y² - y⁴ = c
- x⁴ + x² y² + y⁴ = c
Correct answer: x⁴ - x² y² + y⁴ = c
Solution
The equation becomes d(x⁴/2) + d(y⁴/2) - d(x² y² /2) = 0, integrating to x⁴ + y⁴ - x² y² = c.
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