Suppose y1(x) and y2(x) are two linearly independent solutions of the differential equation x^2y"+(1+sin x)x/2y'-frac32(cos x)y=0, x0 satisfying y2(0)=0. Then which of the following statements are true?

Q91Section C (Part C)91 of 120

Frobenius method — comparing solutions at a regular singular point

Suppose $y_1(x)$ and $y_2(x)$ are two linearly independent solutions of the differential equation

$x^2y"+\frac{(1+\sin x)x}{2}y'-\frac32(\cos x)y=0, x>0$

satisfying $y_2(0)=0$ . Then which of the following statements are true?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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