For $x > 0$, the integrating factor of $\frac{dy}{dx} + Py = Q$ is $x^{3}$. What is $P$?

Explanation

1. 01

   $e^{\int P\,dx} = x^{3}$ means $\int P\,dx = \log x^{3} = 3\log x$.

2. 02

   Differentiate: $P = \frac{3}{x}$.