# What is a particular solution to the differential equation dy/dx=ln x/xy and y(1)=2?

What is a particular solution to the differential equation $\frac{dy}{dx}=\frac{\mathrm{ln}x}{xy}$ and y(1)=2?
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asijikisi67
first separate it
so $y\frac{dy}{dx}=\frac{\mathrm{ln}x}{x}$

$\frac{{y}^{2}}{2}=\frac{{\left(\mathrm{ln}x\right)}^{2}}{2}+C$
put in the IV

$\frac{{y}^{2}}{2}=\frac{{\left(\mathrm{ln}x\right)}^{2}}{2}+2$
${y}^{2}={\left(\mathrm{ln}x\right)}^{2}+4$