Find the general solution to the first order differential equation: ydx + (y-x)dy = 0

Hello!

Let's pick up as the independent variable. Divide the equation by and obtain

 or  

Now divide it by     

Observe that   and obtain  

Now both sides are integrable:

 or   where is an arbitrary constant.

This is the answer in terms of a function of There is no way to express as a function of using only elementary functions.

Hello!

Let's pick up as the independent variable. Divide the equation by and obtain

 or  

Now divide it by     

Observe that   and obtain  

Now both sides are integrable:

 or   where is an arbitrary constant.

This is the answer in terms of a function of There is no way to express as a function of using only elementary functions.