Classifying a Differential Equation

What are the order and degree of the differential equation \(xe^{x}\dfrac{d^{2}y}{dx^{2}}-5e^{x}\dfrac{dy}{dx}+4x^{3}y=0.\) Is it linear?

Solution This is a second-order differential equation of degree 1. Since \(P_{0}( x) =xe^{x},\) \(P_{1}( x) =-5e^{x}\), and \(P_{2}( x) =4x^{3}\) are all functions of \(x\) alone and no term contains more than one derivative, the differential equation is linear.