Solution
$$x^{2}+9y^{2}$$=6xy
$$\Rightarrow x^{2}-6xy+9y^{2}$$=0
$$\Rightarrow (x-3y)^{2}$$=0
$$\Rightarrow$$ x-3y=0
$$\Rightarrow$$ x=3y
$$\Rightarrow \frac{x}{y}$$=$$\frac{3}{1}$$
$$\therefore$$ x:y=3:1
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