How to solve a standard first order differential equation?

First we must ensure that the differential is i the standard form of y' + p(x) y = f(x)The we use the integration factor I(x) = e to the integral of p(x)we then realise that if we differentiate this we will get I'(x) = p(x)* e to the integral of p(x) which is equal to I(x)*p(x)we then multiply the equation through by I(x) giving i(x) y' + I(x)*p(x) y = f(x) I(x)the left hand side can be simplified by the product rule of differentiation and we can then integrate through to find our answer