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.