Given a general first order D.E.
we rewrite it in the form
Now, if M is purely a function of x, and N is purely a
function of y, then we may simply write:
Let
now we can rewrite our D.E. again as
by the chain rule we can obtain
and so we get (noting that
)
and now we integrate (Note: with respect to x) to obtain
Question: what would have happened if we just integrated the equation
Answer: nothing terrible