SOLUTION: Let y be the solution of the differential equation {{{ xdy/dx = y^2/(1-logx) }}} satisfying y(1) = 1. Then y satisfies which following condition: {{{ (i) y = x^(y-1) (ii) y = x

Algebra ->  Test -> SOLUTION: Let y be the solution of the differential equation {{{ xdy/dx = y^2/(1-logx) }}} satisfying y(1) = 1. Then y satisfies which following condition: {{{ (i) y = x^(y-1) (ii) y = x      Log On


   

Question 1184302: Let y be the solution of the differential equation +xdy%2Fdx+=+y%5E2%2F%281-logx%29+ satisfying y(1) = 1. Then y satisfies which following condition:
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Solving the D.E. +x%28dy%2Fdx%29+=+y%5E2%2F%281-logx%29+ satisfying y(1) = 1,

===> dy%2Fy%5E2+=+dx%2F%28x%281-logx%29%29 <===> y%5E%28-2%29dy+=+-d%281-logx%29%2F%281-logx%29

===> -1%2Fy+=+-log%28%281-logx%29%29+%2B+c, after integrating both sides of the previous eq'n.

If y(1) = 1, then -1%2F1+=+-log%28%281-log1%29%29+%2B+c ===> c = -1.

===> 1-1%2Fy+=+-log%28%281-logx%29%29.

Since this answer is not included in the choices, it means that there is some kind of error in your D.E.

You can actually check this by substituting choices (i) to (iv) into the D.E. and will find out that none of them will satisfy it.

Better check again your D.E. and see if you transcribed it correctly.