If I have an equation in the form: dy/dx + f(x)y = g(x)

How can it be solved as y = e^-w * (integral (g(x)*e^w dx) + k) ?

To make it simpler, g(x) = 0, which would make it:

y = e^-w * k

But I still don't see how you arrive at this formula.

Just to be clear, w = integral f(x) dx

Seems to work. If g(x) = 0 then:



If , then substituting in the above yields:



We can substitute for to get:

, as expected.