done a little on using the intergrating factor, but how would be the best way to get the formula into a form to use the intergrating formula?
For a differential equation of the form:
we define as the integrating factor of the differential equation. We solve the differential equation by multiplying through by the integrating factor. so we get the new equation:
it will always be the case that the left hand side is the derivative we would get from applying the product rule. so the equation becomes:
is our solution
remember that you will get an arbitrary constant from the integration, you have to divide this by as well