Differential equation. how to solve?

1. (x^2 + 2xy - 4y^2) dx - ( x^2 - 8xy - 4 y^2)dy=0
2. y(9x-2y)dx-x(6x-y)dy=0; when: x=1; y=1/2

both equation are homogeneous. You can use either of the following substitution:

  1. y = vx
    dy = v dx + x dv
  2. x = vy
    dx = v dy + y dv

The result would be separable equation which you can easily solve. And don't forget to revert back to original variables of x and y then apply boundary conditions as necessary.