- #1

- 66

- 0

y(lnx-lny)dx = (xlnx-xlny-y)

dy/dx = y(lnx-lny)/(xlnx-xlny-y)

y = ux

dy/dx = u + xu'

u + xu' = ux(lnx-lnux)/(xlnx-xlnux-ux)

u + xu' = (ulnx-ulnux-ulnux)/(lnx-lnux-u)

xu'= (ulnx-ulnux-ulnx)/(lnx-lnux-u)-u

xu'= (ulnx-ulnux-ulnx+ulnux+u^2)/(lnx-lnux-u)

xu' = (u^2)/(lnx-lnux-u)

(lnx-lnux-u) /(u^2) *du = dx/x

(lnx-lnux-u) /(u^2)* du - dx/x = 0

Am I correct so far or did I mess up somewhere? Thanks

Edit: I figured out that I had to solve for dx/dy since M(x,n) was simpler and solved the problem.

## Homework Statement

## Homework Equations

## The Attempt at a Solution

dy/dx = y(lnx-lny)/(xlnx-xlny-y)

y = ux

dy/dx = u + xu'

u + xu' = ux(lnx-lnux)/(xlnx-xlnux-ux)

u + xu' = (ulnx-ulnux-ulnux)/(lnx-lnux-u)

xu'= (ulnx-ulnux-ulnx)/(lnx-lnux-u)-u

xu'= (ulnx-ulnux-ulnx+ulnux+u^2)/(lnx-lnux-u)

xu' = (u^2)/(lnx-lnux-u)

(lnx-lnux-u) /(u^2) *du = dx/x

(lnx-lnux-u) /(u^2)* du - dx/x = 0

Am I correct so far or did I mess up somewhere? Thanks

Edit: I figured out that I had to solve for dx/dy since M(x,n) was simpler and solved the problem.

Last edited: