1. ## first order ODE

I would like to solve the differential equation
(x+y-1)dx +(y-x-5)dy = 0
This is not exact. I really cannot figure out the answer.
Anyone can help? thanks in advance.

2. Originally Posted by tszhin8831
I would like to solve the differential equation
(x+y-1)dx +(y-x-5)dy = 0
This is not exact. I really cannot figure out the answer.
Anyone can help? thanks in advance.
first solve the system of equations: x + y = 1, y - x = 5, to get x = -2, y = 3. now let u = x + 2 and v = y - 3. then your equation becomes: (v + u)du + (v - u)dv = 0, which is homogeneous.