The differential equation of the form

${x}^{2}\frac{{d}^{2}y}{d{x}^{2}}+{p}_{1}\frac{dy}{dx}+{p}_{2}y=Q$ where ${p}_{1}$, ${p}_{2}$ are constants and Q the function of x is called Second order homogeneous linear equation.

How can we prove that above equation is second order homogeneous linear differential equation.And also help me to understand the significance of above equation in engineering field.

${x}^{2}\frac{{d}^{2}y}{d{x}^{2}}+{p}_{1}\frac{dy}{dx}+{p}_{2}y=Q$ where ${p}_{1}$, ${p}_{2}$ are constants and Q the function of x is called Second order homogeneous linear equation.

How can we prove that above equation is second order homogeneous linear differential equation.And also help me to understand the significance of above equation in engineering field.