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

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Which of the following most correctly describes the form of the solutions of the differential x2y" + 1/2(x + sinx)y' + y = 0, expanded around x = 0 ? The general solution is of the form y = anxn = a0y1 + axy2, where a0 and a1 are 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 = cos(ln | x |)(1 + anxn), and the second of the form y2 = sin(ln |x|)(1 + =bnxn). There are guaranteed to be two, linearly independent solutions, the first of the form Y1 = cos(ln | x |)(1 + anxn),y2 = There are guaranteed to be two, linearly independent solutions, the first of ihe form y1 = sin , and the second of the form y2 = In There are guaranteed to be two, linearly independent solutions, the first of the form y1 = cos(ln | x | ) and the second y2 = aln There are guaranteed to be two, linearly independent solutions, the first of the form Yl = sin , and the second of the form y2 = aln | x | There are guaranteed to be two. linearly independent solutions, but their form is not listed here. We have covered no theorem, that guarantee the existence of solutions to this equation at x = 0.

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