How to Use The Integrating Factor Method for Differential Equations
The order of a differential equation is determined by the highest order derivative involved! Therefore, first order differential equations consist only of a function and its derivative.
A first order differential equation can be written as
You solve these types of equations using integrating factors.
The integrating factor is eF(x), where
and F′(x) = f(x) without C.
By using the product rule, you see that
This is what you want to introduce into the original equation. Then the differential equation can be solved by integrating factors.
Solve the differential equation y′ + 2xy = ex by using integrating factors