Consider the following differential equation: $x(y \mathrm{~d} x+x \mathrm{~d} y) \cos \frac{y}{x}=y(x \mathrm{~d} y-y \mathrm{dx}) \sin \frac{y}{x}$ Which of the following is the solution of the above equation ( $c$ is an arbitrary constant)?

(A) $\frac{x}{y} \cos \frac{y}{x}=c$

(B) $\frac{x}{y} \sin \frac{y}{x}=c$

(C) $x y \cos \frac{y}{x}=c$

(D) $x y \sin \frac{y}{x}=c$

Consider the following differential equation: $x(y \mathrm{~d} x+x \mathrm{~d} y) \cos \frac{y}{x}=y(x \mathrm{~d} y-y \mathrm{dx}) \sin \frac{y}{x}$ Which of the following is the solution of the above equation ( $c$ is an arbitrary constant)?

(A) $\frac{x}{y} \cos \frac{y}{x}=c$

(B) $\frac{x}{y} \sin \frac{y}{x}=c$

(C) $x y \cos \frac{y}{x}=c$

(D) $x y \sin \frac{y}{x}=c$

Consider the following complex function: $f(z)=\frac{9}{(z-1)(z+2)^{2}}$ Which of the following is one of the residues of the above function?

(A) -1

(B) $9 / 16$

(C) 2

(D) 9

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