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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.
- 49
- 16
- 25
- 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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