Differential Equation, Substitution?

1. Oct 19, 2011

vsportsguy

1. The problem statement, all variables and given/known data
Find the particular solution to the differential equation
(x + y - 4)dx - (3x - y - 4)dy = 0
that satisfies the initial condition y=1 when x=4

2. Relevant equations

3. The attempt at a solution
It's not a homog. or equal D.E., therefore I think it's substitution. I don't really know how to get this problem started.

2. Oct 21, 2011

obafgkmrns

You can simplify the equation by substituting z = y + x. (Note that y = x is a solution for the initial condition x=1, y=1.) However, I don't think you'll be able to find an analytic solution. Numerical solution suggests some pretty funky behavior between 1.84 and 1.85.