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For x >= 0, let y = y(x) solve the differential equation (x + 1)dy = ((x + 1)² + y - 3)dx with y(2) = 0. Find y(3).

1. 3
2. 5
3. 9
4. 13

Correct answer: 3

Solution

Solving the linear ODE gives y = x(x+1) + 3 + C(x+1); applying y(2)=0 gives C = -3, so y(3) = 3.

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