Properties of the Integrating Factor Method

The integrating factor is given by $e^{\int P(x)\,dx}$.

Multiplying by the integrating factor allows the left-hand side of the equation to be written as the derivative of $e^{\int P(x)\,dx} * y$.

After multiplying by the integrating factor, one can integrate both sides to solve for $y$.

Multiplying the entire equation by the integrating factor $e^{\int P(x)\,dx}$ eliminates the derivative term from the equation.