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

Jun 30, 2016

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

#### Explanation:

first separate it

so $y \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\ln x}{x}$

$\int \mathrm{dy} \setminus y = \int \mathrm{dx} \setminus \frac{\ln x}{x}$

${y}^{2} / 2 = {\left(\ln x\right)}^{2} / 2 + C$

put in the IV

${2}^{2} / 2 = {\left(\ln 1\right)}^{2} / 2 + C \setminus \implies C = 2$

${y}^{2} / 2 = {\left(\ln x\right)}^{2} / 2 + 2$

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