Which statement would be correct: "All homogeneous ODEs are also an exact ODE" or "All exact ODEs are also a homogeneous ODE"?

Question

I was asked by my math teacher, but so far couldn´t find the correct answer "All homogeneous ODEs are also an exact ODE" (A) or "All exact ODEs are also a homogeneous ODE" (B) ?

Someone knows any theorem that could prove A or B ?

I assume that one of the statements is correct, from what I understood there is not a "none of the answers above" solution.

Answer 1

None of the above I'm afraid.

Example 1: (2x+3y+4)dx + (3x-6y-5)dy=0 is not homogeneous but exact.

Example 2: x^3dx + yx^2dy=0 is homogeneous but not exact.