The differential equation dy/dx = (x-y+2) / (x+y-2) can be transformed using the substitutions x = X and y = Y + 2. The correct form of the resulting equation is (Y^2) + (2XY) - (X^2) + A = 0, as provided by the author. The alternative solution presented, (Y^2) + (2XY) - (X^2) + A(X^4) = 0, contains an error likely due to incorrect application of logarithmic properties, specifically the rule log a - log b = log(a/b).
PREREQUISITESStudents studying calculus, particularly those focusing on differential equations, as well as educators looking for examples of substitution methods in mathematical problem-solving.
Hint: check how you applied the rule ##\log a - \log b=\log \frac{a}{b}##.foo9008 said: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?
