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Let y = y(x) solve the differential equation x dy/dx + 2y = x² with y(1) = 1. If y(1/2) = k, find the value of 16k.

1. 49
2. 16
3. 25
4. 12

Correct answer: 49

Solution

Solving gives y = x²/4 + 3/(4x²); substituting x = 1/2 yields k = 49/16, so 16k = 49.

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