# Chapter 6 - Differential Equations - 6.4 Exercises: 5

$y=2x^{2}+x+\frac{C}{x}$

#### Work Step by Step

$\frac{dy}{dx}+(\frac{1}{x})y=6x+2$ Integrating factor: $e^{\int(\frac{1}{x})dx}$ $e^{\int(\frac{1}{x})dx}=e^{lnx}=x$ $xy=\int$x(6x+2)dx $\int$x(6x+2)dx=2$x^{3}+x^{2}+C$ $y=2x^{2}+x+\frac{C}{x}$

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