Please see below link for the two different styles of solving a separable equation. http://en.wikipedia.org/wiki/Separation_of_variables#Ordinary_differential_equations_.28ODE.29 Which one is more proper? Why? My DE teacher told me that strictly speaking it's wrong to use the first method because infinitesimals do not have the same properties as other algebraic quantities and therefore can't be multiplied across then canceled so simply. Thank you for your time. This is driving me crazy. I don't like to do my homework until I figure out the details.