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Which of the following most correctly describes the form of the solutions of the

ID: 3081944 • Letter: W

Question

Which of the following most correctly describes the form of the solutions of the differential equation x2y" - x(2 + x)y' + (2 + x2)y = 0, expanded around x = 0 ? The general solution is of the form where do and a0 are a1 arbitrary constants and the solutions y1(x) and y2(x) are linearly independent. there are guaranteed to be two, linearly independent solutions, the first of the form y1 = , and the second of the form y2 = |x| There are guaranteed to be two, linearly independent solutions, the first of the form y1 = and the second of the from y2 = ln |x| There are guaranteed to be two, linearly independent solutions, the first the form y1 = and the form y2 = There are guaranteed to be two, linearly independent solutions, the first of the form y1 = and the second of the form y2 = There are guaranteed to be two, linearly independent solutions, the first of the form y1 = and the second of the form y2 = There are guaranteed to be two, linearly independent solutions, but their form is not listed we have covered no theorems, that guarantee the existence of solutions to this equation at x = 0.

Explanation / Answer

the ans is = d

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