Explain why it is always possible to express any homogeneous D.E.

Explain why it is always possible to express any homogeneous D.E.  in the form  you might start by proving that:  

Any homogeneous O.D.E can be written as   because when identifying our functions of F(x,y) such that:  because our M corresponds to y and N corresponds to x. We add those two functions together and set the equal to zero and we would then get our “Total Differential”: dF=0. Then our solution would be 

When trying to find out if an equation is homogeneous, we must understand what an equation must look like to be homogeneous. A homogeneous differential equation is also an “exact solution,” because it has our last variable,  .  Also worthy of note, a homogeneous differential equation will be any solution where  .

If a function was to not be equal to 0 then the differential equation would neither be homogeneous or exact.

*Note, in most physics equations, we would change out the y variable for ‘t’ (time).