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Решите задачу:

$xy'+2y= \frac{1}{x} \\\\y'+\frac{2}{x}\cdot y= \frac{1}{x^2} \\\\y=uv\\\\u'v+uv'+ \frac{2}{x}\cdot uv= \frac{1}{x^2} \\\\u'v+u(v'+ \frac{2}{x}\cdot v)= \frac{1}{x^2} \\\\a)\; \; \frac{dv}{dx}+\frac{2}{x}\cdot v=0\; \; ,\; \; \int \frac{dv}{v}=- \int \frac{2\, dx}{x} \; \; ,\\\\ln|v|=-2\, ln|x|\; \; \to \; \; v=x^{-2}=\frac{1}{x^2}\\\\b)\; \; \frac{du}{dx}\cdot \frac{1}{x^2}=\frac{1}{x^2}\; \; ,\; \; \int du=\int dx\\\\u=x+C\\\\c)\; \; y= \frac{1}{x^2}\, (x+C)\\\\y= \frac{1}{x} +\frac{C}{x^2}$