# How to you find the general solution of ylnx-xy'=0?

Nov 22, 2016

$y = {C}_{1} {e}^{\frac{1}{2} {\left({\log}_{e} x\right)}^{2}}$

#### Explanation:

This is a linear homogeneous differential equation. Also is separable. So grouping variables,

$\frac{y '}{y} = {\log}_{e} \frac{x}{x}$ After integration

${\log}_{e} y = \frac{1}{2} {\left({\log}_{e} x\right)}^{2} + C$ so

$y = {C}_{1} {e}^{\frac{1}{2} {\left({\log}_{e} x\right)}^{2}}$