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If y = y(x) is the solution of the differential equation, x dy/dx + 2y = x² satisfying y(1) = 1, then y(1/2) is equal to:
- 7/64
- 1/4
- 49/16
- 13/16
Correct answer: 49/16
Solution
The correct option is derived from solving the given first-order linear differential equation using an integrating factor, which leads to the solution that satisfies the initial condition y(1) = 1. Evaluating this solution at x = 1/2 yields the value 49/16.
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