The techniques are:

1) Reduction of order.

2) Homogeneous Linear Equations with Constant Coefficients.

3) Undetermined Coefficients: Superposition Approach.

4) Undetermined Coefficients: Annihilator Approach.

5) Variation of Parameters.

6) Cauchy-Euler Equation.

7) Solving systems of Linear Differential Equations by Elimination.

Q#1: A Search an interesting physical model which can be represented as an ordinary differential equation. Explain it's working in detail and estimate exact solution by the listed techniques