Question Title: “Higher Order Linear Diff. Equations: Coefficients, Non-homogene

Question Title: “Higher Order Linear Diff. Equations: Coefficients, Non-homogeneous Terms, and Applications”
Question Details:
Homogeneous Differential Equations: Explain the concept of higher-order homogeneous differential equations with constant coefficients and their general solutions.
Non-homogeneous Differential Equations: Discuss higher-order non-homogeneous differential equations with constant coefficients, including various types of non-homogeneous terms (eax, sin ax, cos ax, polynomials in xn, e axV(x), and xnV(x)).
Method of Variation of Parameters: Illustrate the method of variation of parameters to solve non-homogeneous differential equations.
Cauchy’s Linear Equation: Describe Cauchy’s linear equation and its application in solving differential equations.
Legendre’s Linear Equation: Explore Legendre’s linear equation and its significance in solving specific types of differential equations.
Application 1 – LCR Circuit: Analyze the LCR circuit model and derive the differential equation governing the circuit’s behavior.
Application 2 – Simple Harmonic Motion: Investigate simple harmonic motion and derive the differential equation representing this type of motion.