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Find the equation of the curve through the origin that satisfies (1 + x²)*dy/dx + 2*x*y = 4*x².

1. (1 + x²)*y = x³
2. 3*(1 + x²)*y = 4*x³
3. 3*(1 + x²)*y = 2*x³
4. (1 + x²)*y = 3*x³

Correct answer: 3*(1 + x²)*y = 4*x³

Solution

Since d/dx[(1+x²)y] = 4x², integrating gives (1+x²)y = (4/3)x³ + C; the origin forces C = 0, so 3(1+x²)y = 4x³.

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