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## Homework Statement

dy/dx=-ylny/x initial conditions y(x=1)=1

express answer in the form f(x,y)=0

## Homework Equations

## The Attempt at a Solution

i let u=ln y

du/dy=1/y

y*du=dy

subbing into equation gives int(y/yu du)=-int dx

which is equal to int(1/u du)=-int(1/x) dx

ln (u)=-ln (x) +c

subbing back in for u gives ln(ln (y))=-ln (x)+c

ln (y)=1/x +c

when x= 1 y=1

ln(1)=1/1 +c

0=1+c

c=-1

equation becomes ln(ln(y))=-ln(x)+c

rearranging (here I am concerned that i make a mistake but I am not sure)

ln(ln(y))+ln(x)+1=0

thank you for your time

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