Answer to Question #235138 in Differential Equations for Kaye

Question

In x dx/dy=2/xy^3

Answer 1

Given $(ln x) \frac{dx}{dy}=\frac{2}{xy^3}$

It can be written as,

$(xln x){dx}=\frac{2}{y^3}dy$

$\frac{2}{y^3}dy = (xln x){dx}$

Integrating both sides,

$-\frac{1}{y^2}=[\frac{1}{2}x^2\ln \left(x\right)-\frac{x^2}{4}] + C$