First integral/general integral

[romsofia]

Homework Statement

Find general integral of {(y+z)Z_x+yZ_y=x-y}

Homework Equations

{pZ_x+qZ_y=r}
{f(u_1,u_2)=0} (u1 and u2 are first integrals, this is the definition of a general integral)

The Attempt at a Solution

I identified p=x+z, q=y and r=x-y, I'm thinking I might have to do something with integral curves to find the first integrals, but I don't how I would do that.

Thanks for any help!

 

[romsofia]

Had a brain fart when I asked this haha, forgot that {dx/p=dy/q=dz/r} (posted this just incase someone googles a similar problem and sees this thread).