Differential Equation, Substitution?

[vsportsguy]

Homework Statement

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

Homework Equations

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.

 

[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.