Solution 3.

First, check to see if    is a homogeneous function of degree 0.

Since   is homogeneous a function of degree 0 we can construct the solution to the D.E.

We are done !

Aside.  We can guide Mathematica to simplify the solution  H[x,y] = c. This is just for fun !

Aside.  We can use Mathematica to make a contour plot of the solution.

Aside.  We can use Mathematica to check to see if the implicit solution is correct.  This is just for fun !

The formulas for  y'[x]  are the same, so our solution is correct.

Aside. We can have Mathematica find the explicit solution to the D.E.  This is just for fun !