Form differential equation by substituition

[foo9008]

Homework Statement

dy/dx = (x-y+2) / (x+y-2) , by using x=X and y=Y+2 , form a differential equation .

Homework Equations

The Attempt at a Solution

the author gave the answer as (Y^2) +(2XY) -(X^2)+A= 0 , while my answer is (Y^2) +(2XY) -(X^2)+A(X^4)= 0
is there anything wrong with my answer?

 

[Samy_A]

Homework Statement

dy/dx = (x-y+2) / (x+y-2) , by using x=X and y=Y+2 , form a differential equation .

Homework Equations

The Attempt at a Solution

the author gave the answer as (Y^2) +(2XY) -(X^2)+A= 0 , while my answer is (Y^2) +(2XY) -(X^2)+A(X^4)= 0
is there anything wrong with my answer?

Hint: check how you applied the rule $\log a - \log b=\log \frac{a}{b}$.