Yet another way to find the solution of

is to seek a function such that the result of multiply (1) by , namely

can be written as

,

i.e.,

where is *a* constant.

Or,

since .

Let us proceed to find such .

From (2) we see that if

then the left side of (2) is certainly and consequently for ,

or,

where is a constant.

Therefore, *a* solution to (4) is

where . This is a positive function indeed.

With (5), (3) becomes

where .

In fact, for any constant c,

is a solution of (1):

Therefore, the solution of (1) is

where is *any* constant.

Exercise: prove that is a positive function.