http://en.wikipedia.org/wiki/Linear_differential_equation
please see the First order equation
A linear ODE of order 1 with variable coefficients has the general form
Dy(x) + f(x)y(x) = g(x).
Where D is the differential operator. Equations of this form can be solved by multiplying the integrating factor
So my question is : why we multiply a integrating factor and how can we know multiply integrating factor in this step but not in other steps??