Differential Equation, nonlinear, nonexact

[MeMoses]

Homework Statement

\frac{dy}{dx}=\frac{2y - x + 7}{4x - 3y -18}

Homework Equations

The Attempt at a Solution

I tried using v = y/x and got nothing. Same goes for trying to find an integrating factor to make the equation exact. I am given a hint, Find h and k so that the substitution x = u+h, y=v+k transforms the above to a homogenous differential equation. I'm not sure what the means or how I'm supposed to use that. Thanks for any help.

 

[LCKurtz]

Homework Statement

\frac{dy}{dx}=\frac{2y - x + 7}{4x - 3y -18}

Homework Equations

The Attempt at a Solution

I tried using v = y/x and got nothing. Same goes for trying to find an integrating factor to make the equation exact. I am given a hint, Find h and k so that the substitution x = u+h, y=v+k transforms the above to a homogenous differential equation. I'm not sure what the means or how I'm supposed to use that. Thanks for any help.

Do you see why the v = y/x method didn't work? Do you see why the $\frac{M(x,y)}{N(x,y)}$ functions aren't homogeneous? Can you use the given substitution to get rid of the 7 and -18?